Working in scale

For those who are new to working in scale and need some basic advice or just a simple explanation before starting, here is an overview. What I’ve often found is that although the principle of reducing an object in size is a very simple one, many people who haven’t done it before may assume it’s more complicated than it is.

If you’re new to it, you can for example decide to make a model or a drawing of something using a simple reduction that can be calculated pretty much in the head, such as ‘half the size’, which means you only have to divide each measurement of the original by 2 (or in other words ‘in half’). If that’s still way too big for your purpose, it is just as easy (if you normally use centimetres) to calculate ‘tenth of the size’ by moving the decimal point of each original measurement by one place or ‘hundredth of the size’ by moving it a further place. You can even quite easily arive at ‘twentieth of the size’ by moving first the decimal point one place then halving! So already you’ve got the choice of four possible scales .. 1:2, 1:10, 1:20 or 1:100 .. which can be done fairly easily in the head! I’ll come back to why they’re written this way (at least, when using metric) later. But what if none of these size reductions, in other words scales, give you the size of model you want or allow you to fit drawings on standard sizes of paper? What if you reckon you need something in between, such as ‘twenty-fifth of the size’ or as it’s written, 1:25 which incidentally has established itself, at least here in the UK, as a comfortable scale for theatre design models and technical drawings? Most people would have to use a calculator to divide by 25 and doing this for each and every measurement would be painfully laborious! At some point in the past someone had the bright idea that having, as it were, a miniaturised version of a long tape measure to read from would save a lot of time .. and so the scale ruler came to be. Most people who regularly have to model or draw in scale use one of these to avoid mistakes even when the reduction is a simple one.

None of us are strangers to dealing with scale, and we deal with it all the time .. everything we see, we see in scale! Unless our eyes are glued up against an object, we see that object at a distance, which makes the image we receive of it smaller than lifesize. We are so used to this that we don’t .. we can’t afford to .. think about it consciously. When we see an object at a distance we don’t question that every dimension of that image (not only height but width etc.) is reduced according to the same proportion or ratio, that is, if the image we receive is half the height that it actually is the width will also be half and the size of every detail will also be half, etc. Everything is divided by the same amount .. in this case by 2. In everyday life we don’t have to be conscious of exactly how much smaller than life-size that image is, but in a way our unconscious mind is and uses that calculation to help judge how far away that object is. Also when practised artists do life-drawings from a model at a little distance from them they usually don’t have to take a tape measure to the model, reduce all those measurements by the same proportion and map out the figure on the paper like a technical drawing. They use the natural awareness of scale we all have to gradually piece together a scale drawing freehand, relating the size of first one part of the figure to another or the general whole to the details, and so on. In other words, we all have a very natural and in-built sense of scale, which we use all the time.

So you could describe this smaller size in a number of ways i.e. you’re seeing it ‘half as big’ or ‘half-size’ or even ‘twice smaller’! That’s where one of the first problems starts, because although I’d guess that most of us understand the phrase ‘half as big’ immediately, we may have a moment’s difficulty with ‘twice smaller’ whereas ‘ten times smaller’ becomes actually easier to understand. The ‘official’ language of scale (the way it’s officially expressed) attempts to avoid the kind of language difficulties which occur between speakers of the same language, let alone between different languages! Also, when recording measurements, it is accepted that anything to do with measurements should be written, not as words, but numerals.  So ‘half-size’ would be written as 1:2 (spoken as ‘one to two’) where, in a way, the colon dots are just replacing the dash in ‘1/2’ when written as a fraction. So, as another example, 1:25 (spoken as ‘one to twenty-five’) should be more easily understood as just saying ‘1/25’ i.e. the drawing or model is ‘one twenty-fifth’ the size of the original .. or ‘twenty-five times smaller’. I find that often the insecurity that many people have when getting used to working in scale for the first time comes mainly from the way it’s written or referred to i.e. that it’s not totally clear what either the two dots or the ‘1’ (or the ‘to’ when spoken) mean here. Understanding it as just a different way of writing a fraction, ‘1/25’, may be one way of understanding it better.

In accepting exactly why it’s written then as ‘1:25’ rather than ‘1/25’ one has to understand that the colon is there to convey that it’s a ratio, in other words a fixed relationship. People who do a lot of mouldmaking and casting .. or people who do a lot of cooking! .. are used to these. For every ‘certain number’ of eggs in a pudding mix there has to be another ‘certain number’ of spoonfulls of flour. Every ‘certain number’ .. in this case a baseline 1 .. of centimetres you measure on your piece of card becomes, means or relates to 25 of the same in the real thing you’re modelling. For the moment we’re staying with metric i.e. centimetres and metres, but I will be speaking about Imperial inches and feet later.

So let’s look at a standard scale ruler suitable for working in 1:25 scale and see how it helps. Above is the most common and easiest type, a ‘triangular’ rule which is able to present six different scales for us, one on each of it’s six edges. These scale rulers usually include 1:20, 1:25, 1:50, 1:75, 1:100 and 1:125 ( the 1:100 ‘scale’ is basically just a regular centimetre rule in which the centimetres can be read as metres. In any event it’s useful to have a regular rule included ). The usual plastic type above has a different colour (green, red, black) to assist in finding the relevant face more quickly. These cost between £6 and £10 in the UK at the moment. The metal one behind it, found in a cheap DIY tool shop, costs a lot less and does its job just as well, but the calibrations wear off a lot quicker because they’re just printed on.

Both clearly show the scaled size of 1metre, 2metres and so on .. up to 7.5metres. Both clearly indicate 50cm divisions and the smaller divisions after that represent units of 10cm. The very smallest divisions within those .. this is important to remember .. represent 2cm each, not 1cm since this would be too small to display. With the right scale ruler to assist, working in scale really should be as simple as reading from a regular tape measure.

But unfortunately one might have to hunt around a bit for the right scale ruler to use. Many art or graphic supply shops stock them but there may be more demand for the type shown above (which is also available in the triangular form) which is calibrated for working in much smaller scales. The numbers along the 1:2500 scale above are the number of metres represented and the smallest divisions therefore represent 2metres. As ‘luck’ would have it this can be used for 1:25 work in place of the proper scale ruler because the calibrations work out the same .. one just has to think of it as representing centimetres rather than metres. So ‘100’ on this readout is 100cm, in other words 1metre at 1:25 scale. A lot of people find it no problem to mentally switch, but it’s certainly much easier to misread or make other mistakes using one of these and it certainly doesn’t help that there are also usually two different scales cohabiting the same edge, as you can see here. I would recommend that if you can’t get the ‘quality’ scale ruler in exactly the scale you want it’s better to go for a cheaper metal one. In the UK I’ve seen these in £shops and Maplin, sometimes Robert Dyas and B&Q.

A word about ‘describing’ scales i.e. referring to them in the correct way! Above I’ve described 1:2500 as a ‘smaller’ scale than 1:25 .. which is correct!  A 1:2500 scale model of an 8 metre long fire engine will be much smaller than a 1:25 model of the same. But the 1:2500 fire engine may be part of a modelled street which conveys a larger area than a 1:25 model can. Although people often refer to the 1:2500 model as the ‘larger’ of the two, especially if it is physically larger than a 1:25 scale portion, it is better not to because it becomes just another cause of confusion!

How to choose the best scale to work in?

I’m often asked by people ‘What scale should I make my model? .. and I wait patiently for more information to come, i.e. the purpose, the context. Sometimes that’s it, almost as if there’s only the choice of a few acceptable scales in the world. To be fair, there are scales that are more prescribed or advantageous in certain circumstances. Theatre design models in this country are always 1:25 scale. If they were any bigger the model-boxes (representing the whole stage space) wouldn’t pass through doorways. If any smaller they would lose in terms of presence and detail. Puppets for stop-motion animation often range from 1:8 to 1:6 ( or ‘2 inches to the foot’) because generally this is the smallest one can go before losing control or sublety in their movements. Also if one’s working in a medium where colleagues or clients are used to a certain scale is it wise to work against the grain by offering up an unfamiliar one?

What I mean is that, there may be conditions imposed on the scale one chooses but otherwise one has the freedom to choose the most appropriate scale oneself. Often this is more a question of how much space one has, balanced with how much one wants to convey and, especially in the case of a model, how much ‘presence’ one wants it to have. In traditional, hand-drawn technical drawing ‘available space’ starts with the size of drawing board one has and therefore the sheet size. If for example one is drawing up a whole room (whether a theatre set or interior design) the minimum ‘kit’ of information needs to consist of a groundplan and elevations (that is, front-on views) of all walls. It’s ideal if these can all be arranged on one sheet, so that elevations can be quickly related to the groundplan. Best of all is if groundplan and elevations can be arranged on the paper like a hinged box, with the groundplan in the centre and walls folded flat around it. This also means that wall lengths and positions of windows, doors etc. can be taken directly from the groundplan when drawing up, which is important because it avoids the possible mistakes that occur when elements have to be drawn in separation. If you can fit all this on one piece of paper at 1:25 scale then that’s great because you can include quite a bit of drawn detail with it. But often it’s not possible, so for groundplans or general overviews 1:50 is often used in the theatre here (or 1:48 ‘quarter inch to the foot’ in film and television .. and I ‘comment’ on that later!). But the point here is that, although there are common practises ( tried, tested and above all familiar methods) that it is often advisable to go along with, in the end any practical solution that the one doing the work (making the drawing or the model) comes up with (including using a different scale if need be) should be acceptable if the end result communicates clearly!

Working in feet and inches

This, I’m assuming, you’ll do without question/choice if you live in the USA, Liberia or Burma where feet and inches are still the standard units of measurement. This measurement system is known as Imperial. If you live in Germany, or most other European countries, you’ll never have had cause to think in any other way than metric. If you live in the UK, on the other hand .. well, according to Wikipedia we have ‘only partially implemented’ the metric system. That’s a very polite way of putting it!

We ‘officially’ changed from the Imperial system of measurement to the metric in the early 1970s but even school rulers still commonly include inches; many people (even those born since) still refer to people’s heights in feet, and carpenters still refer to ‘two-by-ones’ meaning standard timber measuring 2 inches by 1 inch thick! Here you need knowledge of ‘miles to the gallon’ in order to choose a car, confidence in kilometres if you want to drive it and an understanding of feet and inches if you go under a low bridge! This state of things is classic ‘Heath Robinson’ (or ‘Rube Goldberg’ if you’re Imperial), defiantly British, and what’s more there doesn’t appear to be an end in sight. Whereas former Chancellor of the Exchequer Lord Howe spoke out in 2012 about the ‘confusing shambles’ caused by still using both Imperial and metric systems for different things and called for a complete changeover to metric, on the other hand earlier this year plans were being drawn up for a new primary school curriculum reintroducing more awareness of pints, pounds weight and miles by emphasizing ‘parts’ of the Imperial system once more. Politicians are concerned that young people are becoming increasingly confused .. but as yet there has been no unified action to prevent it!

Whether you call it a defiant ‘freedom of choice’ or just a shambolic mess, one area which illustrates both aspects in the UK is in film and television design. For reasons which I still don’t fully understand it’s still a common practice here to draw up (and therefore model up) set designs in feet and inches. When I’ve asked why, no one has given me a convincing answer! Some say it’s because of the ‘American market’ but what does that have to do with designing and building things here? Others suggested to me (a while ago now) that it made sense because structural timber and plywood sheets for building are still conceived in terms of feet and inches (i.e. the ‘two-by-ones’ I mentioned or the 8ft x 4ft standard size for many sheet materials). But, so what? By now we should all be used to reading 2440x1220mm in place of 8ftx4ft and most of the leading hardware suppliers such as Wickes don’t even put feet and inches on their websites anymore.

But returning ..finally!.. to the main point here, if you are working in feet and inches for whatever reason, you have to use a scale that makes sense with, i.e. conforms to and makes use of, the way feet are divided. Because there are 12 inches in a foot the only scales that will work smoothly will be those that are easy multiples of divisions of 12. You try dividing a measurement such as 3ft 8inches by 10, if you’re not sure what I mean! It would never have occurred to a Victorian craftsman to work in 1:10, 1:25, 1:50 or 1:100. What would have occurred quite naturally would be to make one inch, half an inch or a quarter-inch on their measuring ruler represent ‘1 foot’ giving the scales (as we might describe them now) 1:12, 1:24, 1:48 and 1:96. They would be understood and expressed, as they commonly still are now, as ‘one inch to the foot’, ‘half-inch to the foot’ or ‘quarter-inch to the foot’ and so on .. or even abbreviated to just ‘half-inch’ or ‘quarter-inch’. Scaled measurements can therefore be measured using a regular ruler, up to a point, and as long as the inches on the ruler are divided into quarters and eigths. But it’s easy to miscalculate, because for example if you want to find the length of ’27ft 6inches’ at ‘quarter-inch to the foot’ scale, of course you can do it, but you’d first have to divide the 27 by four, hold that 6inch length on the ruler remembering that it represents only 24 of those feet and then add the remaining three-quarters and one-eighth! Generally only the ‘one inch to the foot’ 1:12 scale is comfortable using a regular ruler and for the others there are .. as I say .. scale rulers .. which make the task easier!

Converting from one scale to another

When I’m working with theatre design students I always advise them to design/plan furniture first by drawing it at a larger scale, such as 1:10, before reducing it on the photocopier to 1:25 for the model. It’s just too small to draw with any control or accuracy at 1:25! But when I ask, as a bit of a test, whether anyone can tell me what percentage of reduction is needed on the photocopier to convert a 1:10 to 1:25 I can almost hear all minds in the room turning to jelly. The answer is 40% .. but how does one get that?

If I ask what the percentage of reduction is for changing a 1:10 drawing to a 1:20 there is usually more response. Yes, it’s 50%, because 1:20 is half the size compared to 1:10. Most of us would be able to work this out using a kind of logic rather than actual division of numbers because it’s a simple relationship, but let’s see whether the numbers themselves can be used to give us the same answer? Divide the ‘destination scale’ 20 by the ‘start scale’ 10 and we get 2, which in this case represents how much smaller it is i.e. ‘twice as small’ or ‘half size. Divide 2 into 100 and we get 50, which can now be used as a percentage. So does this work for any set of numbers or is it just a lucky coincidence?

Going back to the previous question, converting 1:10 to 1:25 .. dividing 25 by 10 gives 2.5 (1:25 is more than twice smaller than 1:10). If 100 is then divided by 2.5 it gives 40, so 40% .. which is right! Does it work the other way? Enlarging a 1:25 drawing to make it 1:10 scale? .. dividing the ‘destination’ 10 by the ‘start’ 25 gives 0.4. Dividing 100 by 0.4 gives 250, which is right as 250% on the photocopier.

So the ‘formula’, i.e. trying to write it to remember better, is

destination /divided by/ start  = Y

100 /divided by/ Y = percentage

In fact, this starts off much the same as the way to calculate any enlargement or reduction using actual measurements. For example if one just wanted to change the length of something from 8cm to 13.5cm and wanted to find the percentage .. 13.5 divided by 8 gives 1.6875. But here instead of dividing this by 100 it is multiplied by 100 (just moving the decimal point) giving 169% rounded off. If you divide it by 100 instead by mistake, you get the percentage of reduction needed to convert in reverse, from 13.5cm to 8cm. Usually when doing this kind of thing I don’t analyze the process that much.. all I need to know that I have to divide the larger number by the smaller if I’m enlarging, and the smaller number by the larger if I’m reducing.

For this reason, i.e. because I know I haven’t got the kind of mind that stays in complete control of the logic or the maths in these situations, I asked my father just to check that I wasn’t missing something obvious. Before he retired he was, quite literally, a ‘rocket scientist’ and worked as an aeronautical engineer in the aerospace industry. Although I know this is nothing compared to calculating trajectories I needed his clear perspective.  He pointed out that the ‘formula’ above could be simplified even further by just rearranging it like this

start  /divided by/ destination X 100 = percentage

So make a note of this (much simpler) formula whenever you need to change the scale of something or reduce/enlarge to a specific size.

Making a scale ruler for other scales

Having the formula above, together with either a standard scale ruler (or clearly defined normal ruler) and access to a photocopier, means that one can easily create one’s own custom scale ruler no matter how ‘peculiar’ the chosen scale might be. For example, puppets for stop-motion animation are often made to the scales 1:6 or 1:8. But one can’t buy a scale ruler which deals clearly with these scales. Some might argue that since these scales are derived from ‘feet and inches’ (1:6 is just another way of writing ‘2inches to 1ft’ ) the solution is to work in inches and just utilise a standard ruler as a scale ruler. But no, this really isn’t that simple or comfortable! For example if you are thinking about a 6ft 2inch character at 1:6 scale the feet are easy enough to find .. 12inches on the standard ruler .. but the remaining 2inches can’t be marked with any accuracy because inches on a standard ruler are hardly ever divided into twelfths!

I prefer to keep things metric, and all I have to do is photocopy either the 1:10 face of my scale ruler (or the centimetres on a normal ruler) at a different percentage. So for example, if I want to make 1:10 into 1:6 it’s .. ‘start’ 10 divided by ‘destination’ 6 multiplied by 100 which gives 166.66 .. so 167% on the photocopier will be as accurate as one needs to be. I usually spraymount this onto a card or plastic strip, as below, to make it last.

Taking liberties with scale

‘Taking liberties’, by the way, applies to models .. but certainly not to technical drawings! Perhaps I should better ask ‘When is it important to keep to scale, when is it not so important and when is it actually far better not to?’. It depends on the purposes of the model i.e. the use to which it’s going to be put.

Sometimes this is integral to the medium. For example puppets, whether for stop-motion animation or traditional live performance, rarely conform to normal human proportions. If they did their heads and hands would be too small to be easily workable or have enough visual impact especially from a distance. The fact that the puppets have bigger heads and hands in relation to their bodies makes the scaling of settings and props more difficult to decide and it may even have to vary for different elements. For example the height of a doorway would have to be decided by considering the overall height of the puppet and adding a bit. In this case doorway and puppet height have a ‘realistic’ size relationship. But if the puppet uses a telephone as a prop and it’s sized according to this overall height the receiver will look oddly miniscule when held to the puppet’s ear! Scale in stop-motion animation is often a mish-mash and we don’t have a problem accepting that, perhaps because most of us grew up acting out scenarios with disproportionate toys. This fluctuation of scale and proportion is one of the things that gives stop-motion animation its charm.

Contrast this with any design model made to convey the intentions of the designer clearly and accurately, particularly those communicating the use of space. In these cases scale means nothing if it is not consistent! Unless there’s consistency, and in sufficient significant detail there’s little chance of either viewer or designer being able to judge the full effect of those intentions properly. The only freedom from scale in these cases is perhaps the choice of which details of decoration, texture or colour are really significant. For example architectural models meant for final presentation of a design are very precise in terms of measurements but ‘realistic’ colour or texture are often bypassed in favour of a more aesthetic or abstracted finish (such as blank white or wood veneer) which, it is argued, will focus the attention more on form. The case is similar with so-called ‘white card models’ in film or television set design. These models are meant to convey a very clear and accurate idea of, not only the overall amount of space a set will take up but how it can be used for specific things. These include the positioning of actors, actions within the space and the remaining space available to position cameras, lighting and sound equipment. Any obstructions such as pillars, anything jutting out from the walls and even the smallest steps or variations in the floorspace need to be faithfully rendered so that they are not overlooked when filming is being planned. The emphasis is on all the practical considerations and as long as these are served it’s less important for this type of model to look convincing in terms of texture and colour.

Finished set design models for the theatre have a similar function in that they must convey the performance space as clearly and accurately as possible so that all, especially the director, can judge what can be done in it. But traditionally they are also miniature replicas of the set, not only accurate in scale but complete in terms of colour and texture. For these, all details could be considered ‘significant’ .. the disarray of books on a central table, the crumbly matte surface of an ancient wall or the right kind of curve on a tiny rococo chair .. because a set design is the sum of many visual decisions working together. If scale is unintentionally wrong, no decision can be made as to how it’s going to work and unfortunately it can often seem like an ‘all or nothing’ task because just one out-of-scale element in the composition can upset the whole. I say more about the purposes and the benefits of models in theatre design in my post Why make models? from March 6 2012.

I’ve said it can ‘seem like’ an all-or-nothing task at times but In fact there is, and should be, freedom to mess with scale without the model losing its power to convince! I’ve always felt, and said, that clever suggestion often has more power to convince than slavish depiction .. and it can be a lot quicker!  For example, it generally works very well when real sand, or real woods such as obeche, bass or balsa are used to convey those surfaces in the model. Strictly speaking those materials are out of scale but if one were able to render them in exact scale they would hardly be readable! When trying to model trees it would be senseless to do it leaf-by-leaf .. impractical timewise, but in the end the effort would also be counter-productive. We don’t really experience the ‘look’ of real trees leaf-by-leaf, but rather through the general appearance of the ‘clustering’. Leaves are translucent anyway, so any attempt to recreate them with solid materials and paint is rather doomed from the beginning! Trees can be effectively depicted by choosing a material which ‘clusters’ in the right way, rather than read as individual leaves in exactly the right scale or shape. I’m still looking around for the ideal material in translucent greens which can be chopped or granulated but in the meantime my preference is using crushed eggshell shown below which, once applied, can be tinted with watercolours.

Below are photos taken by Marianna Szekely of her model for a film design project in 2012 at Wimbledon College of Art, London. I feel they illustrate how one can be free and ‘painterly’ in tackling the essentials of surfaces and significant detail, but still achieve a result that is as a whole unquestionably real! As in a good ‘Impressionist’ painting, scale and proportion form a disciplined framework upon which surface qualities can be played upon more suggestively.