Wednesday, July 22, 2015

Let's Talk Geometry

So if you think dressage is boring, this post is probably going to be mind-numbing.  But I've seen a bit of confusion/discussion/frustration on blogs and facebook groups about the "geometry" required in the tests so I figured why not spend some time figuring it out.  It's funny that I'm doing this voluntarily, since the only thing I liked about geometry in high school is that my teacher would call my dorm room to wake me up when I overslept.  True story.

Basically, at my level at least, geometry in dressage means the circles are the right size and shape, your corners are corners, and your half circles are half circles.  I'm focusing on training and first levels here, because those are the tests I know.  If you need help on second level stuff and above, well this is definitely not the blogger you should be asking.

First off, we need to talk about the distances between the letters.  As I mentioned last week, I set up my arena letters on cones and walked the distances out myself, just like I would walk out a five stride line.  I think in feet because I'm an American dammit but I'm trying to just make it simple and say one large step = 3 feet = about 1 meter.  So, from the corner to the first letter of each long side is 6 steps, and from that letter to the next is 12 steps.  Like so:

The next time I rode, I walked the distance for a 20 meter, 15 meter, and a 10 meter circle.  I highly recommend doing this.  It really helps visualize and I rode my circles much more accurately when I got on.  I even dragged my heel to make a line in the sand for the 10 and 15 meter circles the first time.  Helped me feel how a correct sized circle should ride.

20 Meter Circles (Training Level and First Level)

So, just to be super confusing and make you feel bad about yourself, the 20 meter circles at the ends of the arena don't go letter to letter.  That would make it easy.  Instead, a 20m circle at the end of the arena goes just past the V/P or S/R line, and the 20m circles at E or B go just short of that line.  To be more precise, the end circles go about 2 steps (2m) past (6m+12m+2m = 20m) and the middle circles stop 2 steps short. (12m-2m+12m-2m = 20m).

The middle circles touch the rail at E and B, which is slightly less confusing. For the end circles, your circles should touch the rail not at a letter, but actually about 4 steps (4m) past the F/R or M/H line.  The midpoint of a 20m end circle is 10m from the end of the ring, so 10m - 6m = 4m.

At this point, you may be thinking, I WAS TOLD THERE WOULD BE NO MATH ON THIS EXAM.  Don't panic, this diagram is pretty helpful:

So if you do your circles to the letters, the middle one ends up too big and the end ones end up squished.  I figured out a way to remember this:  imagine the three sections of the arena (above) are seats on a plane.  Everyone knows the passengers on the end seats take up the arm rests, and the passenger in the middle has to sit with her hands in her lap the whole flight.  So, the circles on the ends take up the arm rests and go just past the S/R V/P lines.  With me?  Yeah?  Okay great.

15 Meter Circles (First Level Tests 1, 2, and 3)

In the 1-1 and 1-2 tests, the 15 meter canter circles are at V and P.  Like so:

(By the way, I took that screen shot of a diagram from the USDF equitests app.  If you show dressage, you need this app.  At $9.99 it's the most expensive app I've bought, but it's worth it I think. It has instructions, diagrams, the actual tests, and you can record someone reading your test, so that you can just play the test in your headphones while you practice and it will be magically timed to you and your horse.  Plus it's much easier to hand someone the instructions to read on your phone, where they can swipe one at a time, instead of pulling up a pdf and asking them to squint.  Which I've done.)

Since the ring is 20 meters wide, 15m circles at V and P go from the rail to quarterline (3/4 of the ring = 15m).  A 15m circle divided in half is 7.5 meters.  That means the circles go 1.5 meters past the midpoint between the letters (since the letters are 12m apart).  So if I'm on my left lead and I turn off the rail at V, I'm aiming for about 1 1/2 steps to the right of center (toward F between P and F), then for the quarterline, then for right of center between E and V.  So far I haven't had any remarks about the size of my circles.

For the 1-3 test, the 15 meter canter circles are at A and C.

So if the ring is 20m wide, I have to be 2 1/2 steps (2.5m) off the rail.  If R/S is 18m from the end, I have to be 3 steps (3m) inside that line as well.  This weekend will be my first time riding this test, so we'll see how we do with our accuracy.

10 meter circles (First Level Test 3)

In the 1-3 test, there are also two 10m circles at the trot, at R and V.  

These circles go to the centerline (half of 20m), and 1 step (1m) inside the midpoint between R/B and M/R or E/V and V/K. When I actually rode these correctly I was shocked to find out that a 10m circle is much bigger than I thought.  I have been making poor Tucker work much harder than he needs to.  

I should also mention that there are half 10m circles in 1-1 and 1-2.  But since they are really just a turn up the centerline with rounded edges, I haven't had much trouble riding them.  Or I guess I should say that's sort of the least of our problems.

If you've stuck it out this long with this post, congratulations. You earned yourself a cute ponyface that I stole from the internet along with every other diagram in this post (if any of these are yours, I'd be happy to take them down, but I was going to confuse the crap out of everyone without visual aids).


  1. These are awesome diagrams! I've always focused really hard on my geometry in tests knowing that I'm not riding the fanciest horse by far and have to squeeze out every last point I can.

  2. This is both awesome and terrifying. I should have known but I never realized how exact dressage is.

  3. My circles always look like eggs! hahaha

  4. Uh. I feel stupid. How is it that I've never EVER realized that the ends of the middle 20m circle do not hit the rail at V/P and S/R????? *Face palm. I always felt that I seemed off but I based that on thinking my circle was off, rather than it actually being off geometrically. Girl. wow. serious face palm.

  5. Super helpful! Since dressage riders are constantly fighting the Magnetic Force the rail exerts upon the horse ("But we're SAFE on the rail. I LIKE the rail.") this is most excellent. You nail it on walking the test. I've done that while hand walking a laid up horse, and also while riding one horse and ponying the laid up horse. Using mind tricks like trying to keep the ponied horse on the correct lines. It all improves our ability to "see" spatial relationships. Not that I can actually Do any of this accurately. We excel at the squirrel.

  6. Ok, we excel at the *Squircle. But we probably excel at the squirrel too.

    1. Ha! Thank you for the giggle. We have definitely had squirrel moments too. Probably at the free walk.

  7. I'll just be over here reading this.

  8. nice! my trainer always tried to break the circles down into equal sized quarters and i'm trying to do all this math (blargh) to figure out how many strides she wanted per arc bc i thought a 20m circle was 6 strides but now i'm thinking 4?? lol dressage is confuzing


Thanks for taking the time to leave a comment. I love reading them! If you have a question, I will make sure to get back to you.