What a Difference an Inch Makes.

My first anxiety about writing this post is that either my Integral Calculus professor (Hi, Prof. Tsuchida!) or my Kinematics professor (Hi, Prof. Koskelo!) will read this and grade it.  I really need to get over these anxieties.

But this article isn’t about calculus or physics.  Well, maybe it is.  Sorta.  Indirectly.  It’s about archery and the way we teach it.

When we see our students anchoring incorrectly, and specifically when we see them do a short-draw, we often tell them, by way of emphasis, that for every inch they short draw, they lose a pound of thrust to the arrow.  But do they?  Had anybody ever actually measured this?  Well, probably.  However, I decided to do some experimenting myself.

Recurve bows – the type we use to teach western traditional archery at San Francisco Archers – are wonderful machine for storing energy supplied by human muscles and giving it all back in the blink of an eye, sending a 20 gram arrow a couple hundred yards down range.  Some minimal Google research indicates that they were invented independently by cultures all over the world, and are much older than the written records.  The engineering of the recurve bow is fascinating, in that the recurve part of it gives the arrow an additional little kick at the end of the process.  I’m not going to worry about that part, because I’m primarily concerned about the beginning of the process.

The claim that “one inch equals one pound of thrust” comes from the approximation that the average beginner bow requires about 25 pounds of tension to pull to 28 inches, which is the standard draw-length, so we estimate that the difference between 27 inches and 28 inches is approximately 28/25 of a pound.  This has always bothered me because the amount of thrust imparted to the arrow would be the force on the arrow INTEGRATED over the distance between 27 and 28 inches, which surely had to be more than a pound.  What is this value?  I had no idea.  I had to measure it.

Using my Martin Hatfield, which has an AMO weight of 40# at 28 inches, and using the fish scale at the SFA clubhouse, I went to work.  Caveat: The fish scale in the clubhouse isn’t calibrated, and the process was rife with human error.  It involved holding the bow at marked intervals while somebody else made a valiant attempt to read the shaky, unsteady needle.  Also, it’s not a beginner’s 25# bow.  I don’t own one, but I believe we can make some easy extrapolations.  I did my best to minimize experimental errors by taking three readings at each distance and averaging them, but we can still only consider the results to be an approximation.

Martin Response

Response of the Martin Hatfield bow. X-axis is draw distance in inches, the y-axis is tension in pounds.

After taking measurements, I used Wolfram Alpha to find the best fit curve.  Turns out the best fit is a quartic, demonstrating that either the response of wood is far more complex and interesting than I imagined, or the data are really funky.  I leave the judging up to you. However, even if we use the linear equation, the numbers do not differ much.

The math is pretty straight forward – we just take the equation for the curve and integrate.  Interestingly, if we ignore friction and other real life messiness, the total amount of thrust imparted to the arrow is shown the integration from 7.5 inches (brace height) to 28 inches of the equation for the curve, which comes out to 465 pounds.  This is how amazing the bow is!  Using just your own human muscles, you can impart nearly a quarter ton total thrust into an arrow with the mass of 20 grams.  And this bow is only half the pull weight of a typical war-bow from eight centuries past!  (Estimates of what constituted a “typical war-bow” will differ depending on your local expert.)

So what’s the difference in an inch?  Integrating from 27 to 28 inches, this comes out to about 40 pounds.  That’s how much total thrust you loose by short drawing by only one inch.

However, it’s not typical for a beginner to short draw by only one inch.  The most common anchoring error we see is the floating anchor, and that would be nearly impossible to measure.  The second most common anchoring error we see is to anchor with the wrist to the chin.  Using my own hand as a model, that’s a difference of about 4 inches in draw length.  If we integrate fro 24 to 28 inches on the curve, we get nearly 150 lbs of total thrust lost.

Granted, this does not take into account different sized people with different sized bows.  However, we can safely start saying to students who short draw, “For every inch, you lose about 40 pounds of thrust.”  A little more convincing, I think.

More on Zombies and Traditional Archery

I still can’t believe that I got into this conversation about zombies and archery. Both topics are trending right now, due in part to a spat of movies featuring heroic archers – Liongate’s The Hunger Games, Pixar’s Brave, and Marvel Comic’s The Avengers. There is, perhaps, some synergistic effects from the London Olympics. You would not believe the circus that our Sunday Public Outreach has become at San Francisco Archers. It has become so popular that we have had to, sadly, turn people away.  There was even talk of giving people pagers and taking reservations. However, the current archery fever will eventually burn out, as it always does.  The typical teenager’s attention will be occupied by the next Hollywood topic du jour, and our Outreach sessions will return to sanity.

As to the popularity of zombies – who knows? They must appeal to some dark corner of our cultural mindset.  I’ve often thought of them as a metaphor for mindless consumerism.  

Image

Norman Reedus as survivor Daryl Dixon on AMC’s The Walking Dead.

So, have you seen AMC’s series The Walking Dead? Based on the graphic novel of the same name, the show follows a small group of survivors of a zombie apocalypse in Georgia, USA. One of the characters, Daryl Dixon, uses a crossbow to both hunt for dinner and to off zombies. In the universe of The Walking Dead, the only way to kill a zombie is to destroy the brain. Don’t think to much on this, just go with it.

I let myself get involved in an online discssion on this topic, and a user who identified himself or herself as a bowhunter commented that the character should use a compound bow, because the rate of fire is much faster.

I agreed, and added that a recurve has an even faster rate of fire, and hitting something the size of a human head from 30 yards (27 m) was a piece of cake, with decreasing probability from there.  

To which the bowhunter gave a surprisingly angry response. “You’re not going to be able to hit somebody in the head using traditional archery at 30 yards!”

Huh? I briefly considered posting this person’s internet ID on the SCA archery forums and other traditional archery sites, but that would be just mean.  

I believe most compound shooters vastly underestimate the value of traditional archery. Many become addicted to the gadgets, and simply wouldn’t have the first idea of how to aim a traditional recurve or longbow, and they simply have not seen good traditional archery.

So, I’m thinking: Why not make a video? Set up a course at the archery range using those styrofoam wig-thingies that look like robot heads, and then invite my trad-shooting friends to show off their skills? Unmarked yardage. Maybe I can even set up a few to move like zombies. I need to think about this some more.

Popularity of Archery still on the increase after theatrical release of Robin Hood.

Newbie archers at the SF Archers Public Outreach program, June 6, 2010

It was decided yesterday that the San Francisco Archers Public Outreach program needs new equipment.  This topic has been cussed and discussed before, but yesterday was the clincher as we had to turn a dozen people away because we ran out of loaner equipment and arrows.  The photograph shows about 1/3 of the crowd that showed up, even on a cool foggy morning.  Fortunately, is was a crowd of mostly adults who listened to instructions well, because the four of us instructors would have gone running away screaming if it had been an equal number of kids.

I mentioned in a previous post the reasons I think  a poor economy is good for archery.  Basically, it’s a lot cheaper than golf.  We have also noticed a trend in the popularity of the sport which follows the release of any popular movie which features archers.  The recent release of  Ridley Scott’s Robin Hood, starring Russell Crowe, is an excellent example.  This is a very adult version of Hood, and so we got a lot of adults at outreach.  But you should have seen all the kids who showed up after the release of The Lord of the Rings.

Of course, it’s relatively easy to get a group of strangers to show up to try archery once.  We measure the success of our efforts by the number of people who continue to show up after the novelty of it wears off, and they realize that they can’t become expert archers in a single morning’s practice.  We know we have them hooked when they ask, “So, how much does it cost for a good bow?”  We get as excited as any drug dealer.

There are easily half a dozen very good archery ranges in the San Francisco Bay Area, and I explained to two women from San José that they could probably find one closer to where they live.  They don’t have to drive all the way to Pacifica to enjoy the sport.  They responded, “But you guys take care of us.”  That had me walking on air for several hours.

There tend to be two kinds of potential archers who show up: The technophiles who start drooling at the sight of the latest Matthews hunting compound, and those who are attracted to the sexy lines of the recurve or the earthy simplicity of the longbow.   The second group takes more attention because, quite frankly, it’s easier to become competent with a modern compound than a recurve or longbow.  For the second group, who are probably getting frustrated with their lack of accuracy, we make an effort to complement their form and point out their improvements.  There is very little in the way of instant gratification in traditional archery.

At the end of three hours, we did a thorough search for lost arrows, put the equipment away, and sat down to discuss our successes and failures.  We gotta get more equipment!

Poor Economy Good for Archery?

There seems to be an upturn in public interest in target and field archery lately.  I don’t have any specific numbers to give you, only personal observations.

It used to be that I could be assured of getting a lane at the Golden Gate Park archery range in San Francisco on a weekday, or if I show up early enough on a weekend.  Not anymore.  The attendance of newbies at the Sharp Park range in Pacifica at the Community Outreach Sundays has increased.  One could simply attribute this to Summer, but that would not follow the pattern of previous Summers.

On the other hand, attendance at organized events is down.  What gives?  We are getting more newbies but losing the established cadre?

The economy may be a driving factor in both of these phenomena.  People are starting to look for recreational activities that don’t involve a lot of money and can be done locally.

We all know how expensive archery equipment can be.  But when you compare the price of outfitting an archer to, for instance, the price of outfitting a golfer, we archers have to admit we have the better part of that deal.  Also, I don’t know any golfers who build their own equipment, and I don’t ever remember seeing a golf club (or a golf ball) that could be considered a piece of art.

We all know that there are some very nice golf courses in the Bay Area.  What most people don’t realize is that there are half a dozen very beautiful outdoor archery ranges within an hour’s drive of downtown San Francisco.   These golf courses can charge up to $60 and more even on a weekday.  That’s about the price I pay for my yearly membership to San Francisco Archers, which allows me to use the range at my leisure.

So, why is attendance at the organized events down?  I believe it’s because people are starting to pick and choose which events they want to participate in.  When times are good, we go to all of them.  Or nearly.  When the price of gasoline is high and the value of the US dollar drops, we only go to our favorites. I won’t be attending the Western States Traditional Rendezvous until the venue returns to California, or I start making much more money.  Hmm. I wonder which will happen first?