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.

Archery Fever

It started with The Hunger Games, and fortunately the movie was so well hyped that we had plenty of warning.  We all remember what happened when Lord of the Rings and Robin Hood were released.

Archery fever.


This is about a third of the people who showed up one Sunday for our archery public outreach

On the first and third Sunday of every month (except December and January), we invite the public to join us for a morning of archery instruction.  They come from all walks of life, with a heavy emphasis on families.  For a five dollar donation, we put a bow in their hand and an arrow in the other.  We check them for left-right eye dominance, we show them how to load the bow, how to stand, how to draw and many of the other minutiae of archery.

On an average day, we’ll see about thirty or forty people, with an even mix of ages and genders.

Then we noticed an increase in teenage girls, and one of the instructors told the rest of us about the books by Susanne Collins.

“This is going to get ugly,” somebody said, though we all smiled.  Like any other addicts, we love to get more newbies.

No sooner did we adjust to the increase caused by The Hunger Games then we were hit with fans of The Avengers.  Then, the final blow, Brave.

We split our normal three hour session into two sessions of one and half hours, bought more equipment and convinced more members to help out with instruction.

And we still had to turn people away.  I hate turning people away.  People started showing up forty minutes early in order to be insured a spot.  Our scorekeeper showed up to register people and give them numbers.

Yes, it’s a lot of work, but it’s a labor of love.  We get a kick out of it when newbies finally put it all together and start hitting the target more than they miss.

Then we bring out The Balloons. Balloons have a magical quality.  You would be amazed at how much a student’s aim improves when there’s a balloon out there, laughing at you with every miss.  Yes, balloons can laugh.  Put one on a target next time you go to the range, and you’ll hear its shrill, mocking laughter every time an arrow doesn’t end its inflated existence.

Finally, it’s noon, and all the students leave and the instructors meet in the clubhouse for the after-action debriefing.  We talk about the students who shined the students who nearly shot their parents, the students who asked about club membership.

We know that Archery Fever will eventually burn itself out, even if the sport at the London Olympics it does enjoy a brief renaissance of popularity.  Eventually, we’ll be able to go back to sane Sundays, when only thirty or forty people show up.

Then somebody – I don’t remember who – mentioned that there’s a new television show this fall which has received a lot of publicity and seems to be very popular.  Revolution. A world with no electricity, and the inhabitants revert to archery.

“We’re doomed,” somebody said with a laugh.

Zombie Apocalypse – Archers on the Run!

I watched a movie on the SyFy Channel yesterday titled Zombie Apocalypse.  I feel like I need to justify this.  I caught the flu and was feeling miserable and wanted something on television that didn’t require too much cerebral effort while I laid on the sofa like a sick puppy.  So I turned on the SyFy Channel and was treated to a marathon of zombie movies.

Though a lifelong science fiction fan and admitted trekkie, I am not a connoisseur of zombie movies, or even of horror movies in general.  I can’t pretend to be an expert giving a review.  I can only give you my impressions of the movie as viewed from my feverish stupor.

This movie has the feel of something that would be produced by a high school student production.  It’s what you’d expect if the English class wrote the script (and not even the honors English class) and the extras were made up of fellow classmates and the family and friends of the production crew; if the make-up was done by the cosmetology students from the community college; if somebody who is good with a Mac did the special effects; if they borrowed a lot of the props and probably built a few in the machine shop, and filmed the scenes in deserted backlots in Toronto.  Somehow, they talked a Hollywood B-lister, Ving Rhames, into starring.  The production budget was raised from a PTA bake sale.

The story follows a group of survivors across the country, trying to make it to the island of Catalina off the coast of California.  Along the way, they kill a lot of zombies, some of them get turned into zombies, and some of them just get eaten.  Oddly, they keep killing the same zombies, though I suspect this had more to do with a lack of extras than the re-spawning abilities of the undead. They do eventually encounter some kewl zombie zoo animals.

The acting isn’t horrible.  It’s what you’d expect from a community theatre.  There is some dialogue designed to get you interested in the characters, but it was written by somebody with the emotional repertoire of a teenager.  The gory fight scenes, which follow one right after the other, fill in where a more expensive movie would have drama.

That’s not to say that I didn’t enjoy the movie.  I was entertained, though sometimes not in the way the film makers wanted me to be.

So why am I talking about a zombie movie?

There were archers!!  Well, sort of.

Some of the survivors were the school archery team of some university (I didn’t catch the name) and their coach.  And, on the screen, their arrows went exactly where they were supposed to.

Allow me to clear my throat here.

I know that the budget was near zero.  But is it too much to ask that they find a real archer who could give the actors a half-hour lesson on how to shoot?  Or lacking that, isn’t there some professional responsibility on the part of the actors to say, “Hey, if I’m going to shoot a bow on screen, I’d better look like I know what I’m doing.”

It was painful to watch these actors playing competitive college archers, demonstrate that they hadn’t held a bow in their lives until five minutes before filming started.

The scenes which show them loosing arrows are almost comedic.   I tried to find online photos of these scenes, but the produces wisely kept them off the internet.  Ironically, there was a bit of dialogue where one survivor asks the other, “Why bows?”

“Because all the ammunition was already taken.  The sports stores still had archery equipment.”

“That’s because almost nobody knows how to shoot a bow!”

Zombie Apocalypse was followed by Resident Evil: Apocalypse (see the connection here?) which I could stomach until the scene where, knowing that the dead once again walked the earth, they decide to take a short cut through the graveyard.

I don’t believe I’ll ever develop a taste for zombie movies.

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?

SCA Archery and the Labors of Hercules

On August 8th, 2009, the Shire of Cloondara, which is the SCA equivalent of San Francisco, California, hosted its annual Debardchery contest, a combination of archery and bardic contests.  As Archery Mistress, I ran the archery part.  It takes pretty much all year to plan and pull this off.

The Hydra from the Labors of Hercules as a homemade 3D target.

The Hydra from the Labors of Hercules as a homemade 3D target.

The theme of the even was the 12 Labors of Hercules, and we made our own targets.  Here you can see the Hydra.  The rest of the targets were painted on cardboard.  We used the Stymphalian birds as speed targets – The archer could shoot as many arrows as possible in thirty seconds.  There were six small targets, about six inches across, places between 5 and 10 meters distant.  The archer had to shoot each target once before shooting any target twice.

Debardchery 2009 Stymphalian Birds target

Debardchery 2009 Stymphalian Birds target

SCA Archery is restricted to traditional archery gear and wooden arrows, however the construction of the equipment is often modern.  After all, it is called “creative anachronism.”  This is due to the fact that “period” archery gear is near impossible to find on the commercial market, and most amateur archers are not comfortable building their own bows.  We’re comfortable making our own period garb, but functional weaponry, not so much.  There is, however, a “period archery” division in inter-kingdom competition. But if we insisted on strictly medieval construction for bows and arrows, we wouldn’t have many archers.  However, if you want to talk about homemade bows, I can publish some posts on that.

We're comfortable making our own period garb.  Functional weaponry, not so much.

We're comfortable making our own period garb. Functional weaponry, not so much.

Medieval women shooting modern bow

We had a record turn out this year.  Thirty-three medieval archers ranging in skill level from “I’ve never held a bow before in my life!” to “Yeah, I practice every day for an hour before work.”  We separated archers as best we could into five separate skill levels.

The distances to the targets ranged from 5 meters to 45 meters.  However, one 12-year old intrepid longbowmen was allowed to shoot from 30 meters max, as his bow was not able to cast 45 meters.

My schedule for the weekend was a simple one: Saturday – Debardchery.  Sunday – the Cupid’s Gate tourney, which is a “mundane” or real world competition.  So of course, I woke up Saturday morning with a fever and a hoarse voice.  One of the Shire heralds was kind enough to be my voice for the day.  However, she couldn’t compete for me in the Cupid’s Gate, so I regretfully did not participate.

2009 Pacific Traditional Rendezvous

Pacific Traditional Rendezvous

Pacific Traditional Rendezvous

Regarding the pin displayed here:  yes, I know that Rendesvous is misspelled.  It doesn’t do any good to tell me.  I didn’t design the pin, and San Francisco Archers isn’t going to spend the money to redo the pins just to correct the spelling.  Any comment that’s left to tell me that the word is misspelled will simply be deleted.

On Sunday, April 19, 2009, the San Francisco Archers hosted the Pacific Traditional Rendezvous, a competition for  traditional archers to show their stuff.   I heard that there were 110 participants, which means that there were easily 200 people when you count supportive family members and those who crewed the kitchen and registration booth and other support services.

I arrived at about 7:30, still a half hour before the sun rose above the hills in the Golden Gate National Recreation Area.  The archery range is generally the coldest place in Pacifica, a village which is renown for a cool and moist climate.  The weather people told us it would be “warm during the weekend” but we have learned to take their prognostications with a pound of salt.  The pre-dawn temperatures probably hovered about 10° C, and most of us were dressed in layers of clothes.  As soon as the sun poked over the peaks, people started shedding cloths as the thermometer started climbing.  And climbing.  And climbing.

I was too busy with the competition to note the high temperature, but we ended up wearing the minimum amount of clothing that’s prudent for walking around the forest shooting arrows at 3-D targets.Bea at 2009 Pacific Trad Rendezvous

We shot two arrows at each of 42 targets, including the Flying Pig and Running Rabbits and the mammoth.  I suspect that we walked about five kilometers over sharply inclined terrain while battling mosquitoes, hot weather, and severe Spring allergies.  We started at 9:00 in the morning, and finished the 42nd target at 3:45 in the afternoon.  I managed to lose only one arrow when I misjudged the distance to a moose who was standing at the banks of Broadhead Lake, and the arrow sailed into the brackish water.  The ducks laughed at me.  I learned that I really need to practice judging distances with larger animals.  Please note that the second arrow went through his foam heart.

I also sorely misjudged how long it would take to get through the course, so as soon as I shot my last arrow, I had to rush home to help get dinner started.  I had no idea what the results where until my friends, Bea (Pictured above) and Estel came for dinner, and informed us that I had taken Second Place for Adult Female Recurve.  And before you think to ask:  Yes, there were more than two of us in that division.  There were either five or six.  I don’t remember which.  The woman who took First Place beat me by 80 points.  That’s okay: she beat me by 100 points, while seven months pregnant, back in September, so I’m catching up to her.  She’s a very hot archer, and there’s certainly no shame in taking second place to her performance.  Congrats, Trish!!

Also, Congrats to Estel for taking First Place in Adult Female Longbow!  Woot!  I don’t know any of the other results yet.