How to measure angles: the guess-check cycle

The best way to draw an angle from life is this Guess-Check cycle:

1-Guess and draw
2-Check and correct
3-go back to 1 if needed

There are many ways to transfer the angle directly, and I'll teach you how, but you should avoid it because your purpose will be to eventually train yourself not to even need measuring. The guess-check cycle reinforces your training each time that you measure an angle. It gives you instant feedback and correction (a pleasant feeling if you got it, a bit of work and frustration if not). That is the best way to learn. By using a checking method that is accurate and reliable you'll develop a guessing ability that is accurate and reliable.

First we'll discuss guessing, then we'll discuss a couple of methods of checking, and also how to simply transfer angles without guessing, but really, guessing is better (and much faster!) than transfer in the long run, so do make an effort to guess.

Part 1: Guessing.

Measuring the angle of the line that connects the shoulder joint to the wrist joint

So, you have a straight line in front of you, that you want to copy. Say it is an imaginary line joining two points on that handsome model on the picture above: say the line joining the wrist to the shoulder. Now, close one eye, take your pencil and raise it to the line you want to copy, aligning it with the two extreme points, in this case the points being the centers of the balls of the wrist and shoulder. (tip: actually, rather than aligning it on top of the points it is usually better to make it parallel to the line that joins them but giving it a slight vertical displacement so that you can still see the points - if you cover them you don't see what you are doing anymore - the picture above shows that displacement, the pencil is a bit below the line being measured). Very important: keep that pencil on a vertical plane perpendicular to your line of sight, that is, don't let it point away from you (you'll have that tendency when trying to copy perspective lines -fight it!)

Now your pencil and the vertical define and angle. Observe that angle in front of you, put it in your visual memory and draw it on your drawing surface. Now check it.

Part 2: Checking

Few books teach you how to measure angles, and those that do are wonderfully vague. Not having an accurate way of checking angles makes triangulation unreliable, so you have to have confidence in your measuring. Over time I have developed many methods - using one or two pencils - to make angle measuring reliable. Here are a few; later we'll talk about some advanced ones, for very acute angles, and some tricks envolving muscle memory.Anyway, here are a few basic grips I came up with.

A) The vertical grip:

Vertical grip

This is a trivial one and only works if drawing on a vertical surface (say, an easel or a small pad you can raise easily when checking angles), but it is very good and fast in that situation. Just raise your pencil again to the line on the model, as you did in the guessing phase, and slide it across the vertical plane, back to your drawing pad, without disturbing the angle. It is pretty easy to do if your pad is vertical. Just use yor shoulder to move, elbow and wrist held fixed. At first you can even keep your little finger on the pad while you measure and then slide across the pad with the little finger serving as a tactile reference of your distance to the imaginary vertical plane.

Transfering the angle without guessing:

If you don't feel like guessing today: you can use the vertical grip to simply transfer the angle, like this: Place a point where you want the line to start  on your pad. Measure the angle and slide the pencil to your pad. Align the pencil (without changing the angle, just move horizontally and vertically as needed) with the dot you made, and let the tip of the pencil touch the paper to make another dot. Join the dots, they will define a line with the corect slope. For safety, check again anyway. Or, you can just trace the lign directly by sliding the pencil along its own length. Again, check it afterwards.

B) The Cross-Grip (works on any drawing surface, not just vertical)

Cross-grip

Checking with the Cross-Grip

I call this one cross-grip: Take two pencils, one crossed over the other. The thumb presses from one side and the soft part of the tips of the other fingers press from the other side, resulting on a firm grip (round pencils are tougher at first - use pencils that have flattened sides). You will find (after dropping some pencils :)) that by moving the thumb you can make those two pencils change angle as you please (if you find this hard then at first you can help the placement with the other hand). Now call the pencil against the thumb the measuring pencil and the pencil that lies against the other fingers the reference pencil. Keep the reference pencil vertical and make the measuring pencil parallel to the line you want to measure. Now the two pencils describe the angle you want and their position is firm in your hand; you can transport that angle to your horizontal, vertical, or tilted drawing surface (or even a surface across the street!) without losing that angle. Now to check your guess, just align the reference pencil with the vertical of your drawing pad, and the measuring pencil should align with your guess. If not, observe the error, correct your guess and repeat.

Transfering angles without guessing, by using the cross-grip:

If you don't feel like guessing today (shame on you) you can just transfer the angle directly: bring the two pencils to rest on your pad. The pencil closer to the pad is the measuring pencil (no accident: that's why I told you to hold the reference pencil against the thumb and not the other way around), so just place it againt the pad (check again that the reference pencil is correctly aligned with the vertical of the pad) and hold it there. Take your reference pencil on your other hand and draw the line by using the measuring pencil as a ruler. Or just draw two points of that line if you don't want to mess up your drawing. Voila, you transfered your angle.

C) The compass grip

Compass grip

In this grip, you use two pencils as a compass (not a magnetic compass, a circle drawing compass!). Now, this grip works in a different way from the others, so pay attention: You take two pencils. Now one pencil - call it the reference pencil- must remain vertical and align with one point of the line you are measuring (for example the wrist on our model) and the other pencil -measuring pencil- tilts in such a way as to align with another point of the line (say, the shoulder of the model). Not that no pencil is actually aligned with the line whose angle you want to measure! No matter.

Now bring the pencils to your drawing and align the reference pencil with the vertical of the pad and make it touch the line you guessed previously. Then the measuring pencil must also touch that line. If not, correct and check again.

Transfering without guessing: this is a very good grip for direct transfer. The fact that you align the pencil tips with the line on the model gives you greater precision. It is also an easy grip to hold and keep stable. Also, very easy to mark the paper: after measuring the angle just bring the pencils to the pad, align the vertical and place the vertical pencil tip where you want the first point to be. Now let both pencils touch the pad simultaneously, and you have two points that, when joined, describe the correct angle.



Coming soon: The chop-stick grip, the double-vertical grip, and the twins grip. (not kidding)