I got an email from a colleague regarding how to deal with shots that are up- and downhill whilst shooting Recurve Barebow. Here is the question:
“I have a question for you. The standard “cut charts” for distances and shot angles used in field archery are based on the mathematical computation of measuring the hypotenuse of a triangle but shooting a level distance (the long leg of the triangle).
“However, these charts don’t work for me because I shoot a wimpy bow with that produces very slow fps arrows (aka slow). Once I go beyond my POT distance (35m), I am shooting an arc, not a straight line. So I end up ADDING rather than cutting the distances.
“Can you or your stable of experts address this in Archery Focus? Is there a mathematical formula I can use? Trial and error (mostly errors) is costing me a lot of arrows…
And here is my convoluted answer and some of the “back and forth” conversation that followed:
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Note The phrase “Once I go beyond my POT (point-on-target) distance (35m) … I end up adding rather than cutting the distances.” made me suspicious that the archer in question used a gap shooting technique beyond her “point on” which would hopelessly complicate the situation. But being fearless, I just plowed on!
Arrows never fly in a straight line; all arrows travel in an arc (technically it is a “decaying parabola”). Some arcs are just shallower than others in that higher arrow speeds produce flatter arcs. This is simply a manifestation of the fact that when you shoot on the level, gravity is acting only downwards (sideways) on your arrow and this fact forms part of the explanation regarding how to adjust for up- and downhill shots. When you shoot up- and down hill, only part of the force of gravity works as it does on the level, and part of it is applied to make the arrow go faster or slower. Think of arrows going straight up or down, Under those conditions gravity doesn’t bend the trajectory of the arrow into an arc at all. Since only part of the gravitational force is making the arrow bent on an angled shot, you need to plan on a sight setting for part of the distance being shot. Here is a standard “cut chart” used for figuring out the horizontal distances to the target (corresponds to the part that gravity is acting sideways to the trajectory).
This is a simplified chart that ignores the arrow slowing and speeding up effects of gravity. Angles are down the left side, distances across the top. A 50 m shot at 35 degrees is basically only a 41 m shot according to this chart.
If you were shooting with a sight, a program like Archer’s Advantage can calculate all of your sight marks for whatever angle you shoot. Since you aren’t using a sight, this gets complicated.
Have you ever seen a “sight tape”? Just in case, I attached a photo. The strips at the bottom of the printout are cut out and attached to the sight bar. You can see from the markings that the spacings get wider as you go to longer and longer distances. Look at the difference between 60 and 70 yards as compare to between 20 and 30 yards.
When one graphs out crawls, though, one gets a straight line relationship between distance and length of crawl. In other words, the difference between any two identical distances is the same amount of crawl.
Now, given that there is that built in distance, you are going to have to do a little gymnastics here.
Once you get to your POT distance, do you shoot off the shelf, aim high, or lower your anchor? (From your question I suspect that you just aim high for distances beyond your POT, a form of gap shooting. This makes things incredibly difficult, though. For the approach I am thinking of, it is better to go to a lower anchor.
The ideal situation (if using multiple anchors) is to have a low anchor (for long distances) and a high anchor (for shorter distances) and a set of crawls for each (actually the crawls for both anchors will be very similar in that the crawl for 5 m/yd less than POT will be roughly the same for both anchors). When you start to shoot up- and down hills, you would use the anchor for the target distance, but you would take a slightly greater crawl (taking a crawl for a closer target). What your cuts will be are roughly the distance calculated as the cosine of the angle of the shot. (This is straight physics and geometry.)
And, as you know, your bow isn’t gonna be anywhere near ideal for all of the assumptions made. So, you are going to have to do some experimentation. (Do you have an angle finder?)
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To which the questioner responded:
“Wow, my head is spinning.
“Yes, I had already figured out through experience that there is a direct relationship between distance and length of crawl.
“This year, once I get to POT, I start using the plunger and rest plate for sighting points. Last year I did different combinations of face walking and string walking and it was too much for me to remember on the FITA Barebow courses, which don’t allow written memoranda. I also had a lot of trouble getting a replicable anchor once I dropped below my upper teeth, because how much tension I had in my lower jaw varied all over the place.
“The other thing I am wondering about is the arrow trajectory and its impact on crawls past POT or at least the zenith of the shot. I don’t think my arrows travel in a nice curve, instead they go upwards most of the way and then drop steeply at the end. I am planning to play around with walk-back shooting to see if I can figure this out, and whether or not it matters.
“What does the last column of your attachment mean? For less than 10m, because I don’t want to crawl anymore, I just aim off a little.
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That’s for people with sights.
When you say “I am wondering about the arrow trajectory and its impact on crawls past POT” you are making me wonder because to go past your POT, there is no crawl. You either aim off (gap shoot) or switch to a lower anchor and crawl down from your new POT.
The system I recommend now is to use the most comfortable anchor you have (this is usually the finger in the corner of the mouth version of a “high anchor”) and figure out your POT(High Anchor) distance and then all of your crawls down (inward) from there. Then, to deal with distances past your POT(High Anchor), you adopt a different, lower anchor (usually the Olympic-style anchor) and find your new POT, the POT (Low Anchor), then you figure out your crawls down from there. If … if … those two series overlap, you are generally good to go.
This has the “feature” that the crawls for the two anchors are generally very close, so five yards inside both the POT(High Anchor) and the POT(Low Anchor) are about the same crawl (why I do not know), so this reduces the amount of memorization.
If there is a gap between the two sets of crawls, we try to bridge that by aiming high off of the POT(High Anchor). All this requires you to know, if there is say a five yard gap between the two series, is what a shot lands at five yard past your POT distance with a zero crawl. If your arrow lands five rings low under those circumstances, then you need to aim one ring high for every yard you are past your POT. (I picked those numbers for simplicity, of course, your situation will be much more complicated (much). ;o)
Every anchor has its own POT distance. And there are all kinds of anchors to chose (you have tried face walking you tell me). The FITA Field experts work like crazy to get a POT of 50 m which is their longest shot (for the unmarked). So they have one set of crawls for the entire course. So, your trepidation was certainly shared by others!
And we have yet to get to the crux of the aiming up and down hills issue.
PS When you shoot with a sight, there is a point in space where the arrow rises up from its position below the line of sight to the line of sight. Typically for me that was around 11 or 12 yards out. (If you check one of those sight tapes I sent you, the tape stops at that point as there are no more markings that mean anything.) When targets are inside of that distance, you have to set your sight for an even higher distance to work. For example, I often set my sight for 52 yards for a 4-yard shot. The arrow is still rising to the line of sight the aperture is in, so the aperture has to be set much higher to get the bow low enough to hit anything. That is what those boldface numbers are on the right side of the AA printout, shooting targets inside your crossover distance.
There is so much more to this discussion, I will follow-up with another post.