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ARCH 1311 Lecture 23 - Video #2: Proportion & Scale — Transcript

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0:02in this lecture we're going to be
0:04discussing proportion and scale the
0:07lecture material is taken from chapter
0:11six in form space and order by Francis
0:16Chang and we're going to be talking
0:19about different elements of scale and
0:22proportion and also comparing them to
0:26some examples of architecture in the
0:29book book and also discussing the
0:32architectural theory behind some of
0:35these
0:37ideas now when we're talking about
0:39proportion and scale they're definitely
0:42related ideas so typically when we're
0:45talking about scale in architecture
0:48we're talking about the size of
0:51something as it relates to something
0:54else so something that something else
0:57might be a human so when we're talking
1:00about human scale in this photo we can
1:04see that there's this large building but
1:07until we start looking at individual
1:11items that give us a sense of how big it
1:13is we are trying to adjust to its scale
1:19so the scale of the humans on the street
1:23the very tiny Glimpse that we get at the
1:26bottom of the photo of some cars
1:30some street
1:32signs um some people kind of in the
1:34foreground and in the background that
1:37gives us a sense of the scale of the
1:39building meaning the size of it in
1:41relation to other reference objects now
1:45those reference objects could be human
1:47beings but they could also be other
1:49buildings they could be other things
1:52that in our mind we know how large those
1:54things are so we can kind of compare and
1:58contrast those with the building that
2:00we're looking
2:02at usually when we're talking about
2:04proportion we're talking about the
2:07relationship of parts of the building to
2:10each other so we might look at you know
2:15one part in relation to the overall
2:18whole meaning does this kind of fit in
2:22relation to what else is going on in the
2:24building is it harmonious meaning do the
2:28parts work together like do the
2:30different uh sizes of the pieces
2:33complement each other or are they kind
2:36of In conflict with each other if we
2:39were looking at the proportion
2:42of the parts of this particular building
2:45we would probably look at the opening
2:48sizes in relation to the kind of pills
2:53or projected columns that are shown we
2:57would look at the uh cornice kind of the
3:01top of it going around and the ballast
3:05Rod that it's sits at top the building
3:09and at the base of each of these upper
3:13level openings so we would start to look
3:16at the measurement of these pieces and
3:19think you know do those look like they
3:22are properly relating to each other
3:25or you know what we would like to do
3:29with the design of these in order to
3:31make them more harmonious or proper or
3:36maybe we want them to be in congruous
3:39but um those are things that we look at
3:41with proportion so proportion is really
3:44looking at the relation of the parts of
3:47the building to each other or to the
3:50overall composition of a facade or
3:53elevation or the overall design of the
3:57building when we talk about
3:59proportionality or proportions one type
4:03of issue that we start to look at are
4:06material proportions so when we talk
4:10about material proportions we have to
4:12look at where are the materials coming
4:14from we use man-made materials we use
4:19natural materials in the course of
4:22constructing buildings and so if we take
4:26one example which would be wood then
4:29wood comes from trees so it's a natural
4:32material and because of that there are
4:35certain proportions that wood can or
4:39cannot have
4:41so first of all the size of it we're
4:44looking at you know a maximum size based
4:48on the size of that tree so the tree is
4:52going to be cut up and if we want a
4:55straight piece of wood taken from that
4:57tree then we've got to get probably
5:00right at the heart of the trunk and you
5:03know you're only going to be able to
5:05extract a certain amount of material and
5:09it's going to have certain
5:12proportions so um when we look at
5:16individual materials each material has
5:19its own properties meaning it's got
5:22certain levels of
5:24hardness uh strength
5:27durability um resistance to the elements
5:32and certainly when we talk about
5:35strength
5:37that's really closely related to
5:39material proportions so if I have a
5:42piece of wood that is you know really
5:46long and it's taken from this one tree
5:49and it's a single cut so I haven't like
5:53glued it or attached it to
5:56other uh pieces of wood or other
5:59material
6:00then that piece of wood can only span a
6:03certain length without increasing in its
6:07width and depth and thickness so if I
6:11have for example a
6:132x4 then that 2x4 is only going to be
6:17able to span a certain distance
6:20lengthwise before it starts to either
6:23sag in the middle or before it starts to
6:27fail or starts to break or crack or show
6:32some signs of weakness and so then if
6:36that's the case and we still have a need
6:38for using that particular material in a
6:42particular application then we would
6:44need to con increase its material
6:47Dimensions or its proportions would need
6:50to increase meaning like once you
6:52increase the length of it then the width
6:55and thickness and depth of that material
6:57need to increase also so
7:01proportionality applies not just to a
7:04whole building but it applies to various
7:06parts of the building so when we're
7:08talking about proportions it's you know
7:10how the parts relate to one another so
7:13it's almost like when one increases then
7:15the others need to increase in order for
7:18it to function properly and the same
7:21thing goes for other materials that are
7:24man-made if I have a brick typically the
7:28brick is going to be longer in one
7:30dimension kind of the elevational
7:33dimension that we typically see at the
7:35side of a building and if that length
7:39were to increase then uh likely the the
7:44depth and height are going to increase
7:46as well now sometimes when you have
7:48something like a brick it has certain
7:51modular proportions meaning um they're
7:54more
7:55standardized uh but wood has that too so
7:58You' have like 2x4 and 2x sixes and
8:00things like that but when we're looking
8:04at those materials as a whole system you
8:07want to make sure that you're keeping
8:10with the proportions that are either
8:12standardized or that will be applicable
8:16to the most
8:18suitable application of that material or
8:21the most suitable use of that
8:24material now sometimes we have material
8:28proportions and and depending on the
8:31properties of the material just because
8:33you increase one dimension and increase
8:36the others in relation to that that
8:38doesn't mean it's always going to be
8:41structurally sound or structurally
8:43viable so for example in the case of
8:46that wood beam if I increase the length
8:48of it I probably need to increase the
8:50depth and width and thickness um and at
8:55some point you're going
8:57to reach a point where you're not going
9:00to be able to cut a beam that's big
9:02enough out of this single tree in order
9:05to get the proper length so then you
9:07might need to make an engineered beam
9:10where you kind of take different parts
9:12of wood and glue it together in a
9:14different way but if you had something
9:17like a stone slab like let's say we had
9:20a slab of granite that we're were going
9:22to put in a countertop
9:25application and usually it that's you
9:29know somewhere between like an inch or 3
9:31in you know maybe it's like an inch and
9:33a half or 2 in so let's say the slab is
9:362 in thick and it's 4T wide by 8 ft long
9:43so at some point you're going to
9:47increase the size to the point where
9:49you're going to need intermediate
9:51supports so maybe you can get about 3 or
9:544T wide and have it unsupported in the
9:58middle but if you keep increasing that
10:01size and you say well okay now I want it
10:04to be 8 ft uh between the supports then
10:09that material based on its thickness and
10:11its material properties would probably
10:13just crack or collapse under its own
10:16weight so it would need to be supported
10:19at intermediate points along its length
10:23the same thing goes for its overall
10:25proportions if you said Okay I want to
10:27make this you know 50 the slab 50 ft
10:31long and you just say well if I want to
10:35do make it 50 ft long I'm just going to
10:37increase its thickness by that same
10:39amount so you know it's not really
10:43practical to say I'm going to have this
10:45granite slab that's 50 ft long and a
10:49foot deep or a foot thick because then
10:52its own weight is so great that it
10:55really can't be supported in uh practice
10:59IAL way and then it starts to crack and
11:02break and collapse under its own weight
11:05so you really want to look at the
11:08properties of the material and then
11:10alter its proportions
11:13or try and make the best application
11:17with the proportions that will be most
11:19correct for its structural needs and the
11:25cost benefit of using that material and
11:29also the best performance and
11:31functionality of that
11:34material when we talk about structural
11:37proportions we're talking
11:40about both visually and
11:43structurally how one material supports
11:46another so this is Stonehenge in England
11:50and this is kind of almost a cartoonish
11:54example of structural diagramming at in
11:59terms of having a post and lentil system
12:03so a post and lenal or a post and beam
12:05system is where the post are the
12:07vertical elements and the beam or the
12:11lentil is the horizontal element and you
12:14can see how in a very simple way these
12:19Stones just based on how they're propped
12:22up and their location and their size are
12:25able to support one another so there
12:27isn't anything else going on except
12:30just these Stones being supported so
12:32when we look at the post stones or the
12:35vertical pieces they're very wide in
12:39fact one of the ones kind of toward the
12:43right of Center is tapered so that it is
12:47a little bit smaller at the top and
12:51increases in width down toward the
12:53bottom and that is a structurally
12:57beneficial shape because the amount of
13:00weight that it needs to support actually
13:03increases as it gets further away from
13:06that post object or further away from
13:08the lentil and needs to be supported
13:11toward the ground so this is almost a
13:16diagrammatic way of showing that this is
13:19structurally
13:21supportive now it's also visually
13:24supportive in that you got these really
13:26heavy chunky pieces of Stone supporting
13:30these other heavy pieces of stone turned
13:32on their side now could you have a
13:35smaller piece of stone supporting those
13:39beams or lentils going across yes
13:42probably but based on you know the
13:46technology that was probably available
13:48and the stones that were available we
13:50think that this is a really uh
13:53acceptable and adequate use of uh this
13:58post and beam
14:00technology and obviously it's held up
14:04for thousands of years so um the other
14:08thing that it shows is you've got these
14:12supportive pieces and then the pieces
14:15that are resting on top that are being
14:18supported end right in the middle of
14:21those posts so you have enough of the
14:24support on either side where they're not
14:27going to fall off it's not going to uh
14:31break down the support piece and they're
14:34they're going to be equally supported uh
14:37at the vertical side and then those
14:39horizontal pieces have enough material
14:42that's
14:43supported uh on their ends so the
14:46structural proportions of
14:49this
14:51are are both structurally useful and
14:56Visually useful so it allows all the
14:58load loads to be
15:00transmitted um horizontally across the
15:03part that's open and then there's enough
15:06support there by the vertical post that
15:09those loads can be transferred down and
15:12when we talk about structural loads it's
15:13just the weight or the actual heaviness
15:17of the object that needs to be
15:24supported when we talk about
15:27manufactured proportions we're talking
15:30about objects that have been created in
15:34a factory condition and they could be
15:38all kinds of materials that are used in
15:40architectural applications so it could
15:42be something like concrete masonry units
15:46like we're looking at here this is
15:48looking at an elevation view of a
15:50concrete masonry unit wall or CMU wall
15:54and those blocks each have definite
15:59standardized manufactured proportions
16:01meaning for its uh overall length it has
16:06a certain height has a certain width and
16:09thickness and the proportions of those
16:13are a one to2 proportion meaning the uh
16:18height of this is half of the width so
16:23what we're seeing there on this side is
16:25you know 2 times the height is the width
16:28and so you have this 1:2 ratio that you
16:32see throughout this
16:34system and you know you have
16:37manufactured proportions in all
16:39different kinds of material so you might
16:42have some series of windows and doors
16:46that are going to be in an architectural
16:48project and those are going to have
16:51definite Dimensions from the
16:53manufacturer because the manufacturer
16:56makes a certain amount of Windows and
16:59have certain amount of sizes they
17:01probably have standard sizes and they
17:04have cataloges that they put out of
17:05their standard sizes and so those
17:09manufactured proportions become really
17:11critical not just for the person
17:14selecting it either the
17:16architecture architectural consultant or
17:19the designer but also for the
17:22manufacturing that they have systems in
17:25place that have determined those
17:27proportions and
17:29those
17:31are the most beneficial in terms of that
17:34material working
17:39properly now there are several
17:41proportioning systems that we're going
17:43to be discussing and some of those
17:46proportioning systems have been around
17:48for a very long time uh this is a sketch
17:51or a drawing done by Leonardo da Vinci
17:55and this is the Vitruvian Man so the
17:59Vitruvian man might sound familiar so we
18:02talked about Vitruvius the architect um
18:07D Vinci drew the Vitruvian Man based on
18:10those principles that Vitruvius laid out
18:13for things that were harmonious and
18:17Visually appealing and functionally
18:19appealing and so you know Vitruvius
18:22talked about firmness commodity and
18:25Delight so the Vitruvian man says there
18:29are certain proportions that relate to a
18:32human being that are going to be uh
18:37delightful and
18:39proportional when that is applied to
18:42architecture so if you have something
18:44that is way out of human scale or much
18:48closer to human scale that the Vitruvian
18:51Man kind of dictates that the things
18:54that are closer to human proportions or
18:56human scale are going to be
18:59uh more harmonious in terms of their
19:04proportion relating to
19:06architecture now there's a lot of debate
19:08about whether this is you know uh the
19:11ideal but there are a lot of
19:14proportioning systems that we can
19:16utilize to kind of check um designs as
19:21we're creating them or if there's an
19:24existing building we can analyze their
19:26proportioning systems to try and learn
19:28learn more about the rules or systems
19:32that they use to design it now one of
19:34the first ones that we talk about is the
19:36golden section and the golden
19:39section is an ordering system that can
19:43be applied to classical architecture
19:46when we talk about classical
19:47architecture a lot of times we're
19:49referring to ancient Greek or ancient
19:52Roman architecture but it can also be
19:54applied to a variety of buildings and
19:58what it says is that you have parts of
20:02the building and again we're talking
20:04about proportions so we're talking about
20:06how different parts of the building
20:08relate to the other parts and it says as
20:13you start to
20:15draw different proportional sizes onto
20:19the building or you start to apply these
20:22kind of
20:24sectional areas that they relate to each
20:27other in a way
20:29that they create ratios so if I look at
20:34you know the one side of this golden
20:37section this one kind of creates a a
20:40swoop so you can kind of create this
20:43curly CU almost looks like a nautilus
20:45shell but basically what you're doing is
20:48you're breaking it down into larger and
20:51smaller rectangles and then measuring
20:53those and seeing if those are
20:56proportional like is it um you know know
20:591 to2 or is it 3 to 8 or whatever the
21:04ratio happens to be you can start to
21:07measure and see if those different parts
21:09relate to one another now in the book it
21:13kind of raises a good point like do we
21:15even know or can we even tell that
21:18something is designed According to some
21:21of these proportioning systems and the
21:23answer is yes on a subconscious level
21:27probably you know you probably aren't
21:29going into a building and saying this is
21:32exactly in keeping with all of the
21:35tenants of the golden section but you
21:38might go into a building and it feels
21:42right to you it feels like it is working
21:46together like the individual parts are
21:49in keeping with each other there aren't
21:51things either visually or spatially that
21:54you're sensing that seem out of uh
21:58proportion or out of scale but a lot of
22:02times that's because the creators or
22:05designers of the building worked very
22:07hard to make sure that the different
22:10parts were proportionally related to one
22:12another so the golden section is one
22:15that can often be employed it's a system
22:18that can be employed to kind of double
22:20check the parts of your building and
22:23make sure that they are relating to each
22:24other in a rational and geometric way
22:28way so sometimes we look at this in a
22:31mathematical way sometimes we look at
22:34this visually but the golden section is
22:36something that can be actually
22:38physically measured uh
22:41mathematically the golden section is
22:43also referred to as the golden mean or
22:47the golden
22:49ratio and this word mean mea n you
22:53sometimes hear when we're talking about
22:55architectural ordering systems or
22:58proportioning systems and literally the
23:01word mean tends to be the midpoint
23:05between two points or two objects um but
23:10here I think we're talking more about
23:13that harmonious balance between
23:16spatially hitting something that is
23:19desirable or proportionally
23:22desirable so the golden mean describes
23:26this curvature that kind of looks like a
23:29nautilus shell here but all that's
23:32happening with this curving line is that
23:35it's forming a continuous line through
23:38these rectangular and square
23:42areas now the other thing that's
23:44happening is
23:46that when we have something like the
23:49golden section is the ordering system we
23:52can find out exactly what the
23:56mathematics are of our proportioning
23:58system system that's why it's often
24:00referred to as the golden
24:02ratio so where does this ratio come from
24:05and how do we figure this out
24:07mathematically so really the golden
24:10section and golden ratio is derived from
24:13Fibonacci numbers and the Fibonacci
24:16numbers
24:18were created or kind of tapped into by a
24:23man named Fibonacci his name was
24:25Leonardo Bonacci some people call him
24:28Leonardo of Pisa he was born in the 12th
24:33century and he was an Italian
24:35mathematician and he's kind of the
24:37father of modern
24:40mathematics and when we look at the
24:42Fibonacci numbers the definition of them
24:46is adding together integers or
24:50sequential numbers and hitting on
24:55certain numbers in a series so the the
24:58way the series works is uh you start
25:01with 0 0 + 1 is 1 and then uh you add 1
25:07+
25:081 and then you add 1 + 2 because those
25:12are those two integers and then you add
25:152 + 3 3 + 5 is 8 and then 5 + 8 is 13 8
25:21+ 13 is 21 you kind of see how this
25:24sequence goes along and when you look at
25:27the bot bottom row when we're looking at
25:31the actual Fibonacci numbers it's 0 1 1
25:352 3 5 8 13 21 and a lot of those are
25:42referenced in patterns or ordering
25:45systems in natural
25:47objects um in things like
25:52flowers uh petals pine cones
25:56leaves um even pineapple skins and all
26:01other kinds of things but the way that
26:05the golden section is derived is by
26:07taking these numbers and creating actual
26:11areas out of them so when we look at the
26:16figure on the right um if your area is
26:1921 or you've got a ratio that it you
26:24know has some number on one side or some
26:27number on the other side and if this is
26:29a square then you have the square of 21
26:32it is equal to both sides of that square
26:35and then you have a smaller Square um
26:38where the area is 13 that's proportional
26:41then that adds up to all of the areas of
26:45the smaller squares put
26:48together and the same is true if you
26:51look at the figure on the left it's
26:53still holding the same proportional
26:56relationship even though the numbers are
26:59different and so that's kind of the
27:02magic of the Fibonacci numbers is that
27:04they're
27:05proportional and um rational in that
27:10those ratios all relate and so you can
27:12kind of keep increasing the actual
27:15number value but those sizes will still
27:19be relating to each other in the same
27:21way and there will still be
27:24proportional so often we refer back to
27:28these numbers when we're looking at uh
27:31things like the Golden Ratio or the
27:34golden section there are other ordering
27:38systems that rely on the logic of the
27:41Fibonacci numbers such as the modular L
27:46corbusier's ordering system
27:49and often when we're looking
27:53to see what will be pleasing and
27:57proportional to the op
27:58it's a little bit deceptive because you
28:00know everyone's perception is different
28:03everyone's perception of space is
28:05different sometimes when we are in a um
28:10rectangular room it can actually seem
28:12Square depending on the width or depth
28:17or height of the room and if we're in a
28:22uh rectangular space it can often seem
28:26longer than it actually is or shorter
28:28than it actually is depending on our
28:30point of view or perspective within the
28:32building so sometimes we go back to
28:35these more rational ordering systems so
28:39that we
28:40can kind of control the perception of
28:43that space a bit better and make sure
28:46that the parts are relating to each
28:49other in a way that is uh mathematically
28:53desirable I suppose or theoretically
28:57desirable and that they relate to each
28:59other and they are uh forming another
29:03hole that is
29:04also you know relating as a ratio back
29:07to those original smaller
29:10areas when we talk about proportioning
29:14systems like the golden section and
29:16there are several like this that we'll
29:17look at but one of the ideas of the
29:21golden section is that you can draw
29:23these lines which we refer to as
29:26regulating lines you can kind of draw
29:28them either on the elevation or the plan
29:31of a building and you can start to see
29:35shapes and sizes that relate to one
29:37another so the this image that's shown
29:41is of notr cathedral in Paris and when
29:46we're looking at this you might see
29:51some architectural ideas like Symmetry
29:55and
29:56proportionality and balance some of the
29:59things that we talked about earlier in
30:01the semester but here you can physically
30:04start to measure like oh okay if I break
30:07down top to bottom the different pieces
30:10or parts of this then you know these are
30:14evenly equally spaced chunks of the
30:17building so that lower kind of entrance
30:21tier of the building is 1/3 of the
30:25overall height and then the middle part
30:27is is another thir so equally spaced and
30:31then the towers are also 1/3 and if you
30:35start analizing it mathematically it
30:38makes more sense that visually it would
30:40seem like it's balanced and had proper
30:44architectural
30:46proportions now if you look at the width
30:50of this or kind of the side to side
30:52elevational relationship of the part
30:55then that also is 1/3 of those
30:59individual pieces now that doesn't mean
31:02that the 1/3 at the top is the same
31:05distance is the 1/3 on the side it just
31:08means that in relation to those other
31:10vertical Parts those are equally spaced
31:13going side to side or left to
31:16right and then on the right we can start
31:20to draw more complex regulating lines
31:23it's basically saying the same thing
31:25we've got these you know third or
31:28equally spaced proportions we can start
31:30to draw these uh diamonds or uh kind of
31:35zigzag lines that all start to relate to
31:37one another and you can start even
31:40within those thirds as you go up you can
31:43start breaking down the individual
31:44pieces like how tall are the archways
31:47how tall are the doorways how tall are
31:49the openings do those relate to other
31:52pieces of the building are they
31:55proportional you know with the other
31:57entrances or with other parts of other
32:01side elevations but those regulating
32:04lines are the actual lines that you
32:06start to draw on top of the drawings of
32:09the building or even photographs of the
32:11building to start to make sense of its
32:16parts and its individual
32:23sizings one thing that we talk about
32:26when we're discussing
32:28classical architecture are the classical
32:31orders and there are five main classical
32:34orders a lot of times you know we'll be
32:37discussing Greek and Roman architecture
32:39when we talk about the classical orders
32:42um but the five main ones that you want
32:46to remember are the Tusk in order that
32:49which is shown on the right this is the
32:51more the most simplified of all the
32:55orders um and then the
32:58Doric order a lot of times people can
33:02remember this best by the type of
33:04columns that are utilized in each of the
33:06orders so the Tuscan column is fairly
33:09simplified at the top and the bottom but
33:12it does have a base at the bottom um the
33:16DOR column is the only one that does not
33:19have a base but is typically a fluted
33:21column meaning it
33:24has um some ridges or ribs that go all
33:28the way around the uh side or the length
33:32of the column and then the other columns
33:36are fluted the ionic Corinthian and
33:39composite column meaning it has the
33:43fluted base or kind of the riged base or
33:46the riged um column but it does have a
33:50base at the bottom so when we look at
33:53ionic it trademark is kind of the curly
33:57cues at the top and Corinthian has the
34:00leaves these acanthus leaves and the
34:04composite column has both so when we
34:06talk about something that's composite
34:07it's typically two materials together or
34:10two parts together and the composite
34:13column combines the capital or the top
34:16of the column at the ionic order and the
34:20Corinthian order
34:23so often times you're going to be
34:26looking at um the type of column that's
34:29used to determine the order sometimes
34:32you'll look at the freeze or the inure
34:35which is the top piece of the building
34:38that is being supported that looks like
34:40a bunch of crown molding but those have
34:43different um features and different
34:47parts that would be associated with with
34:49each of those orders the Doric order has
34:53kind of
34:54a uh patterned in taure p patterned
34:58freeze that has these uh individual
35:01features that relate to one another and
35:03then ionic Corinthian and composite are
35:07very closely related but you can see
35:10that composite really combines all of
35:13the features of both Ionic and
35:18Corinthian there are several Renaissance
35:21theories related to architecture and
35:26proportioning that were employed by
35:28various Architects during the time of
35:31the Renaissance and specifically the
35:33Italian
35:35Renaissance one architect Alberti
35:38designed a church called Santa Maria
35:41Nolla and he utilized different ratios
35:46that were related to the uh Greek
35:50musical system um that were originally
35:55kind of derived by Pythagoras of the
35:58Pythagorean theorem and so there are
36:02different methods that people would use
36:05especially during the Italian ronance to
36:09have something
36:10that was perceived and appeared to be
36:14harmonious but also
36:17felt balanced and
36:20um desirable in a way that maybe hadn't
36:25been specifically defined before and so
36:28you know when we talk about people's
36:30perceptions of space being different and
36:33people's visual perceptions of what is
36:36pleasing as being different then if
36:38you're trying
36:40to make a Common Thread between being
36:45visually and
36:47spatially
36:49appealing then a lot of
36:51Architects during the Renaissance would
36:53start to mathematically try and hit
36:56these certain targ
36:58so that they were kind of sure that over
37:00and over they had something that
37:03spatially felt right and Visually
37:06appeared and and felt right to
37:09them now one architect
37:13who employed these specific Traditions
37:18or these specific types of proportioning
37:20systems was Andrea padio and in that
37:24previous slide that we saw that was the
37:27PO Ian uh Villa
37:30rotunda and he was
37:34influential for a variety of reasons but
37:37in uh his book The four books on
37:41architecture he followed in the flip
37:43steps of Alberti which was one of his
37:46architectural predecessors and he
37:50proposed these ideas for the most
37:53beautiful and proportionable manners of
37:56rooms that was kind of his idea and
37:59so he had a theory that the heights of
38:04rooms could be
38:06determined by the width and length of
38:10the room and so that there was a
38:13proportional equivalent that would feel
38:16spatially correct when a person was in
38:20the room so he had kind of three
38:22different methods of determining that so
38:25um if we break it down mathematically
38:27there's the arithmetic uh mean the
38:31geometric mean and the harmonic mean
38:35now what that says is in the uh in the
38:40first kind of theory that rooms with
38:44flat ceilings should be equal to their
38:47width the height of rooms of flat
38:49ceilings so if you had a room that was a
38:52certain length and a certain width and
38:54it had a flat ceiling then that meant
38:57meant that you should have uh a height
39:00that was equal to the width so that's
39:03saying that's kind of that arithmetic
39:05version where it's like if if C is kind
39:08of the Wild Card component that's not uh
39:11the length then um then the width and
39:15height should be equal to one
39:18another um now if you had a square room
39:23that had a vated
39:25ceiling then the height of that room
39:28should be 1/3 greater than the width and
39:32this is all pilo you know using his uh
39:36theorem so that's kind of the geometric
39:39approach where you
39:41have uh the height that's um 1/3 greater
39:45than the width and so that would uh give
39:48you a greater sense of space above you
39:52and you know because the sides were
39:56proportionally Square then you would
39:59have enough height kind of above you to
40:01make it feel like the the room wasn't
40:04kind of crushing down on
40:06you and then in the harmonic
40:10mean um it talks about
40:14utilizing uh Pythagorean theorem and
40:18Pythagoras's theory of means to
40:20determine their heights based on the
40:23extremes of the width and length of the
40:25room so uh that was a bit more variable
40:29but that depending on any type of room
40:32size you could mathematically determine
40:36the ideal proportion for the height of
40:39the room and so it really introduces the
40:43idea
40:44of spatial integrity and
40:49spatial uh
40:51Beauty in a way that doesn't just
40:54address the plan it doesn't just address
40:57the elevation it takes the whole spatial
41:01experience of being inside of a piece of
41:04architecture and trying to really Target
41:07what is uh what is most beautiful um and
41:12what is most pleasing and beneficial in
41:14terms of experiencing that space or
41:17experiencing that
41:24building the modular is is another
41:28proportioning system that is based on
41:33several of the things that we've talked
41:34about it's based on Fibonacci numbers
41:38it's based on the golden ratio the
41:41golden
41:43section and this was created by the
41:47French architect Lor buer and um the
41:51earlier part of the 20th century and
41:55it's kind of taking a lot of those those
41:58uh previous theories of
42:02proportionality and incorporating them
42:06into not only the architecture but
42:09relating them to parts of the human body
42:13so this sketch and you know this is a
42:17quite a famous drawing in
42:19architecture sometimes people refer to
42:21this as modular man so the modular is
42:25this system but modular man is you know
42:29hitting these individual parts of the
42:32human body and saying okay there are
42:34these proportions from uh you know the
42:37bottom of your feet to your waist and
42:40then up to the top of your head and then
42:43you know from your elbow to the top of
42:45your fingertips if your arm were raised
42:49now obviously this is not Universal and
42:52it's not universally applicable because
42:55people have all different dimensions and
42:58shapes and sizes yet relating it back to
43:03the scale of human beings at least gets
43:06a target for what is going to
43:10be more in keeping with human beings and
43:15human scale you're if you are designing
43:18to the modular you can have a building
43:22that's actually quite large and a really
43:25complex facility but if the space is
43:27within it are relating Back To Human
43:32sizing then you can have many people
43:35occupying a very large space and still
43:39make it feel like you're not overwhelmed
43:41by the building and it's still designed
43:44for you as a
43:45human now lorier kind of tried out this
43:49theory in several of his buildings but
43:53uh one that he is particularly known for
43:56is is
43:58the uh unite dehabitation in um France
44:04and it's because it was a fairly
44:08large kind of apartment buildings but it
44:11was a housing complex and so if you took
44:13the housing complex and just looked at
44:15it as a whole kind of Chunk it's
44:18actually quite a large facility that
44:20could be very overwhelming if you looked
44:24at it in terms of a human but the
44:27interior spaces because they related
44:30Back To Human scale the experience of
44:34going through those different spaces it
44:36doesn't seem overwhelming and in fact
44:39can house many people comfortably
44:43instead of um making the the building
44:46seem like it's the kind of
44:50um you know brutal large object that's
44:55kind of swallowing people up so relating
44:57to the human body proportions and also
45:00the functional dimensions of a human you
45:02know like where your knees are where you
45:04might bend at the waist where you're um
45:08you
45:08know comfortably sitting and he had some
45:12other sketches where he showed you know
45:14someone sitting at different you know
45:17Heights depending on their task like if
45:19you're were sitting close to the floor
45:21and perhaps reading or if you were
45:23sitting and eating or standing with your
45:27arms folded or you know standing
45:29reaching up so modular man is standing
45:32and reaching up because that's kind of
45:34the extent of what would be uh
45:39comfortable or what would be necessary
45:41in terms of spaces relating to humans so
45:45once you get past where people are able
45:47to reach then you're kind of out of the
45:50zone of what is functional and
45:52proportional for um people in using a
45:57particular
46:03space the other thing that lorier did to
46:07apply this Theory to his
46:10architecture and again at the UN dataton
46:15and
46:16Marse he used the strategy of placing
46:20windows and placing openings where they
46:23would be related to people performing
46:26different functions within the building
46:28so instead of just looking at a building
46:30as an isolated object and kind of
46:33looking at it from the outside and
46:34saying okay here's the elevation of the
46:36building I'm going to put a bunch of
46:38Windows like this because I like the way
46:40they look as a building he really you
46:43know placed people inside of this
46:46building and there are little openings
46:48kind of all over and if you look at his
46:51drawings it shows people you know
46:54sitting and reclining and then you can
46:56look out and have a view from that place
47:00where you're sitting or you could be
47:02walking upstairs and looking out um you
47:06can be um kind of standing walking past
47:10and then have a window at head height so
47:13all of these things kind of relate back
47:15to you as a human so that you're
47:19experiencing the
47:20building uh in all your various
47:23activities and it doesn't seem like the
47:26placement of Windows or the placement of
47:28opening is arbitrary and more related to
47:31the building but it's more related back
47:33to the occupants or the inhabitants
47:36inside of
47:42it um the next ordering system that we
47:45look at uh comes from Japan and it's
47:51based on a traditional Japanese
47:54measurement unit and that measurement
47:56unit is the
47:58shaku and um originally was actually
48:01imported from China and it's very close
48:05to the English foot and it's um
48:09divisible by decimal units but if we
48:11kind of look at this in terms of how
48:14many
48:15shaku the individual unit is then that's
48:20that's typically how people measure this
48:23so um there
48:27there are kind of two different methods
48:29that we look at when we refer to the Ken
48:33and the Ken is
48:37um it's not just a measurement for the
48:40construction of buildings but it it's
48:43also uh an aesthetic or visual module
48:47that orders how Japanese architecture is
48:51structured how it functions and where
48:55partitions are placed or where openings
48:57are placed and so it's a very rational
49:00system based on the number of these
49:04individual units that can be placed in
49:07there okay so there are kind of two
49:10different ways of looking at this so the
49:13um the Ken you can look at it as a
49:16modular grid system and it's uh you know
49:21developed in a couple of different
49:24ways and so the the first way that we
49:28look at it uh it's the inaka method or
49:33the tatami
49:35method uh there's a standard tatami
49:38floor matat so when we're looking at
49:40these individual rectangles that go
49:43together that's a standard to Tommy
49:46floormat and the proportion of this is
49:50basically 1 by two so it's a 1x two
49:53module meaning the width is
49:57half the length or the length is twice
50:00the width so depending on you know how
50:04however you measure it um it's roughly
50:083et by 6 feet give or take but it's 3x 6
50:12shaku so that's the the measuring uh
50:16unit and so in the first method uh the
50:20floor mat VAR
50:23slightly when you have interrupt
50:27or columns or other things that
50:31are placed within the building so you
50:34might alter the mat to kind of move
50:36around that column or you might move
50:39around that particular partition and you
50:43might even vary it slightly to
50:45accommodate the thickness of something
50:48that it's
50:49touching um
50:51and you know the tatami method while it
50:55has these these m at is a is slightly
50:58more variable and then the kioma method
51:03is much more constant so it's quite a
51:06bit more measurable and um a bit more
51:10rigid because the floormat size in the
51:13kioma method remains constant and it's a
51:183.15 by 6.3 shaku
51:22Dimension and um then instead of
51:25changing the floor mat to accommodate
51:27the column spacing their column sizing
51:30the column spacing changes to
51:34accommodate the um the size of the room
51:39and the uh shaku so the size of the room
51:43is designated by the number of floor
51:45mats so the floor mats really dictate
51:48kind of everything that's going on in
51:50the room um now they can be arranged in
51:55many different ways and so sometimes a
51:58room is described by how many mats can
52:01be placed in the room so there's uh a
52:05three mat room if we look at it kind of
52:08on the left um this the next one is a
52:114.5 mat room so you have kind of this
52:15pin wheel effect then there's a six mat
52:18room an eight mat room a 12 mat room and
52:21these just kind of keep adding on to
52:23each other and you can see that the
52:28proportions of these start to kind of go
52:31back and forth so there's like uh this
52:34proportional rectangle and then a square
52:36and then a rectangle and then a square
52:38and then a rectangle and then as you
52:40keep adding depending on what side you
52:42add them to you're going to come up with
52:44a square or kind of a proportional
52:47rectangle so it's a really interesting
52:50system and you know we look at
52:54traditional Japanese architecture
52:58to show either one of these methods
53:01either the tatami the matte method that
53:04um kind of varies to accommodate the um
53:08columns or partitions typically it was
53:10an open space so there's usually a room
53:13with columns um or the kuma method where
53:17you have the maths really driving how
53:22the space is designed and how the room
53:25designs at operates and how it
53:33functions
53:35anthropometry
53:40is
53:42anthropometry is the study of the human
53:46body and it refers to the measurement of
53:51the size and proportions of the human
53:53body so when we're talking talking about
53:57using anthropometry as a design tool we
54:02are really using the human body to drive
54:05a lot of the design choices within a
54:08space or within a
54:11building and we're looking at things
54:15like how do people function within a
54:17space where do they sit uh where do they
54:21stand how do they stand you know where
54:24are they looking what are the their
54:26visual perception how much can they
54:29rotate their head what's their
54:31peripheral vision I mean it really gets
54:33into how people perceive space and how
54:37they utilize
54:39space uh now there's also another field
54:44of study that is developed based on
54:47anthropometry and that's ergonomics so
54:50that's kind of the applied science that
54:53coordinates um the design of
54:57environments and architecture and
55:00systems that really are in concert with
55:06our psychological functions our
55:09physiological and physical
55:12functions anthropometry often looks
55:15[Music]
55:16at different people and different groups
55:19of people and how they utilize space uh
55:23sometimes we look at persons with with
55:26disabilities and how they are able to
55:29access specific spaces how we can design
55:32things so that they are most accessible
55:35to most people and we're not limiting
55:39who can use a space based on your
55:42physical
55:43ability and so anthropometries is
55:46critical in terms
55:48of commercial construction and just
55:52modern construction that allows for the
55:55greatest number of humans to be able to
55:59use any particular space now when we're
56:03talking about residential spaces you
56:06might be looking at something that is
56:09much more customized and much more in
56:13tune or designed to a specific
56:15individual and in that case the
56:17anthropometry measurements can be much
56:20more specific sometimes you know in
56:23commercial construction or buildings
56:26that are designed for a large number of
56:28people we're trying to look at averages
56:31average sizes of people um the ability
56:36of most people regardless of ability or
56:39disability to be able to use a space but
56:43in the design of a a very specific
56:47private space like a residential space
56:49you can get into a
56:52person's actual sizing actual ability
56:57and it becomes much more customized but
57:00it's really the general study of the
57:03human body and what you're able to do
57:07physically and how you also perceive
57:09things psychologically so not just where
57:12things are placed although it involves
57:15that but it can also involve things like
57:18color how we perceive texture the
57:22tactile nature of buildings how we're
57:24able to move throughout the space uh
57:28where lights are placed and appliances
57:32and fixtures and you know walking
57:35surfaces and all kinds of things so it's
57:38a really kind of
57:40extensive system for
57:43proportioning meaning you're just
57:46measuring everything and you know how
57:48far someone can reach to open a door or
57:52how much they can turn their arm or turn
57:55their hand in order to open a door so
57:58it's something that is is really
58:01extensive but also really helpful to the
58:04designer to be able to
58:07reference all of this information and
58:09data and incorporate it into the
58:11building so that is as functional and
58:15beneficial as possible to the greatest
58:17number of
58:23people when we talk about scale
58:27typically we're talking about a building
58:30or something in relation to something
58:33else outside of it so when we're talking
58:35about proportions we're talking about
58:38how the building relates to itself or
58:40how the parts of the building relate to
58:42each other but with scale we're talking
58:46about you know how it relates to an
58:49unrelated or reference object now
58:52sometimes that reference object is a
58:54human being that's why we kind of talk
58:57about anthropometry as a proportional
59:01tool but it kind of leads us into the
59:03discussion about scale so
59:07scale you know often is something that
59:12we can't perceive unless we have a
59:15reference object so for example this is
59:18um a building that Frank Gary had done
59:21several years ago and there this is a
59:23sculpture of binoculars that
59:26incorporated as an installation into
59:29that building and unless you can start
59:33to see reference objects like you know
59:36if if the woman were not standing in
59:38front of the binoculars you might be
59:40able to look at the windows and start to
59:42figure out how big these binoculars are
59:46but with her standing there you can see
59:48exactly how big they are you know
59:50because our mind perceives a person
59:53within a range of heights you know
59:56unless she's a 35t tall person we're
1:00:00going to be able to tell visually and
1:00:03kind of let our mind know how big this
1:00:07is and that's kind of how scale works
1:00:09you're always searching mentally for
1:00:12something that is referential or
1:00:14something that makes sense to you so
1:00:16that you can tell how large or how small
1:00:19something
1:00:24is one type of scale that we look at is
1:00:27visual scale so again as we're
1:00:31perceiving a building as we're looking
1:00:33at it this is um notom cathedral in
1:00:37Paris if we didn't have all of the
1:00:40people at the very bottom of the
1:00:42photograph and we didn't have the
1:00:45buildings on the two sides then it would
1:00:49be more difficult to visually place the
1:00:54scale of the windows of this church it
1:00:57would be difficult to place the scale of
1:01:00the doors
1:01:01even because there are sculptures of
1:01:04Saints running along the tops of the
1:01:08kind of bottom three arches and those
1:01:11are not necessarily the size of actual
1:01:14people so again that's a little bit
1:01:17deceiving and even the doors if you
1:01:20didn't have actual people there you
1:01:22might think those doors are like the
1:01:25size of of a person when in reality
1:01:28instead of those being like you know 6'
1:01:308 or 7t tall doors they're probably five
1:01:34times that size and you know the size of
1:01:39an actual person is about 1/5 of the
1:01:44total height of those Central doors in
1:01:47that Center Archway so visual scale
1:01:50gives you
1:01:52some uh reference pieces and reference
1:01:56points that allow you to understand
1:02:00visually and mentally and
1:02:04psychologically how big or small things
1:02:08are um now some buildings can have
1:02:11multiple scales operating simultaneously
1:02:15so the the towers you know if those were
1:02:18isolated in your mind you're thinking
1:02:20how big are these right how how large is
1:02:24this uh thing
1:02:26and it's really in proportion to other
1:02:30elements of some known size so then
1:02:34you'd start to maybe work your way down
1:02:35to the building maybe start to look at
1:02:37the doors but having the person or
1:02:41people there in relation to the doors is
1:02:43what really allows you to understand the
1:02:46building and understand how big it
1:02:52is now human scale you know
1:02:56visual scale can reference something
1:02:58that is an either a human or non-human
1:03:02object uh but human scale is what really
1:03:06lets you understand what that space
1:03:09might potentially be like to an habit
1:03:12and so when we're looking at the drawing
1:03:15on the left this is what we'd refer to
1:03:18as kind of monumental scale so that
1:03:21Archway is much larger than a person but
1:03:25you can't tell that until you see the
1:03:28people in the drawing and if you didn't
1:03:32have that then you might think that
1:03:34Archway was like twice as tall as a
1:03:37person instead of 15 times as tall as a
1:03:40person and so that human scale really
1:03:43helps you understand what the building
1:03:45is like in relation to a person now the
1:03:49the kind of section cut on the right is
1:03:53is much more scaled to the size of an
1:03:56actual human and so when we look at this
1:04:00you can start to understand what it
1:04:02would be like sitting in that chair on
1:04:04the second floor and reading the
1:04:07newspaper with that lamp overhead or
1:04:10because you can see this man kind of
1:04:12walking into the first floor you can
1:04:15understand what that would be like for
1:04:18the roof overhang to be just over your
1:04:22head by a couple of feet so human scale
1:04:25definitely helps us
1:04:27understand what that space might be like
1:04:31in
1:04:32uh in relation to humans um now of all
1:04:38the dimensions when we're talking about
1:04:39rooms of all the dimensions that affect
1:04:42human scale and human perception the
1:04:44most it's typically the height because
1:04:49if the height of room is too low then
1:04:54physically we feel feel like it's almost
1:04:57coming down on us and if it's too high
1:05:03then you might feel like the room is
1:05:07kind of overwhelming or it's kind of has
1:05:09a silo effect like um like it's too tall
1:05:14uh but the ver that vertical dimension
1:05:17of space typically affects people's
1:05:20perception of a room more than altering
1:05:24the other dimensions so for example if
1:05:26we had a room and it was a certain
1:05:28length and width and height if we
1:05:31increase the width by a foot people
1:05:34wouldn't notice it as much as if you
1:05:36increased or decreased the height of the
1:05:39room by a foot um because it's that
1:05:42spatial perception that is is most um
1:05:47felt by humans when they're entering a
1:05:51space some other things that can affect
1:05:55the scale or the human scale of an area
1:05:58are the color um of its surfaces the
1:06:04patterning or texture of its
1:06:06surfaces uh the shape of the openings
1:06:09within the surfaces for example if a
1:06:13wall uh if there are four walls in a
1:06:16room and the height of the ceiling is
1:06:18very tall if there are large openings
1:06:20then it doesn't feel as confined because
1:06:23you feel like you've got space around
1:06:25you or you could move into an adjacent
1:06:28space um or if there are fixed elements
1:06:32within the space that's going to affect
1:06:34how humans perceive the overall
1:06:36experience of the
1:06:43space scalar comparison just means that
1:06:46you're literally comparing the the scale
1:06:50or shape or size of one building with
1:06:54another and you know sometimes when we
1:06:57look at large buildings these are tall
1:07:00buildings um then you might think well
1:07:04well this building is is fairly tall but
1:07:08um you know there's no human
1:07:11scale that's shown in this diagram we're
1:07:15just looking at the comparison of tall
1:07:17buildings to tall buildings and
1:07:19so because they're all you know um quite
1:07:24Grand in scale and quite Monumental in
1:07:27terms of human scale to put a person in
1:07:30any of these would be um almost a little
1:07:34speck right because they're um
1:07:37comparably so so small in comparison to
1:07:41these other buildings but we're talking
1:07:43about comparing scale or scalar
1:07:45comparison it just means that we are
1:07:48relating one object to another one
1:07:50architectural building or architectural
1:07:53object to another to see uh how it
1:07:57Compares size-wise and also its you know
1:08:02features in relation to one another

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