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.



Sometimes persistence is the answer. (Especially if the clue is “obstinate assiduity.”)

Any ride you can crawl away from.

I have been having more than my fair share of flat tires lately.  It’s not as if I’m actually aiming for the broken glass and nails and such so much as they are hunting me down.  And they must be stealth nails, because I rarely see them.

December 30th – Scheduled my last long ride for 2012.  Started off by asking Google to show me a bicycle route from Brisbane, California to Tiburon and back – a metric century. Why consult with Google Maps, you might ask?  Don’t I already know the way?

Well, yes.  However, the bicycle option for Google Maps has often suggested interesting routes I would not have otherwise considered.

This was not to be the case on this day.  In fact, as I perused the suggested route, I came across item #36: Turn left to stay on the Coastal Trail.  Take the stairs.

Take the stairs? Just what part of bicycle did Google not understand?  A friend suggested that perhaps it thought I was asking for a cyclocross route.  Other than those stairs, Google’s route was the same as I’d’ve taken without inquiry.

On the road by 9:00 because I wanted to get back before dark, everything went according to plan until I sauntered into Sausalito.  Started out on the Mill Valley-Sausalito path and suddenly there was a lot more friction in the road than I liked. Looking down, I could see that the recumbent’s front wheel was in the process of going flat.

Damn.  Another one.

Pulled over and pulled out the fix-it kit, which included both patches and a spare tube.  I decided on the spare because that would be faster.  I could patch the old tube when I got home.

Back on the road — Yes!! Much better!  Cranked the velocity up to about 20 mph to take advantage of the flat path and windless day.  Went about a mile and then …

thump thump thump thump …

Before I could finish the thought, What the hell is that thumping?  POW!

The front tire failed explosively and I went tumbling, as my father would say, “asshole over appetite.”  The asphalt rose to slap me in the face and I blocked it with my right hand.


Whose idea was it to make asphalt out of such rough material?

Sliding several feet on hands and rump, all I could do was grit my teeth.  When the sliding stopped, I waited on all fours like a dog for the first wave of intense pain to pass.  After about three centuries, it did, and I picked myself up off the road.  Other cyclists were starting to gather.

“You okay?” they seemed to ask in unison.

Hmm.  Was I okay?  Quick check for broken bones and bleeding.  Seems I was able to protect all my favorite organs.  “I’m fine.  I think the bike is broken, though.”

Aside from the tire, the rear derailer lever was broken off.  That’s going to be fun.

Having assured them that I wasn’t going to pass out nor bleed to death, the other cyclists went their way, and I pulled out the fix-it kit again.

The new inner tube failed at the valve stem weld.  So now I have to patch the old inner tube, anyway.  Maybe I should write a letter of complaint to the tube manufacturer?  Would it do me any good?  Didn’t seem likely.

I had intended to meet a friend for lunch in Tiburon.  After explaining my delay by cell phone, we changed the lunch to Mill Valley.  Riding there, I discovered I could only change the cassette gears with great difficulty.  Effectively, I was stuck using the three gears available on the chainrings.

I needed to accomplish two things: Expedite the trip home and avoid the slog up the hill from Sausalito to the Golden Gate Bridge.  Fortunately, both of these were attainable by taking the ferry from Sausalito to San Francisco.  From there, it was relatively flat to Brisbane.

Except for one hill.  Third Street to Bayshore, near Candlestick.  I decided on an alternate route going around Candlestick Park, which was longer by a mile or so, but much flatter.

Little did I know that the 49’s had a game that day.  Hey, I’m not a football fan.  I hope they won and all that, but there I was, navigating around the aftergame traffic, police barriers, street vendors, and drunken fans on three gears.

Life is good!

ALC Training ride from Tanforan to Stanford University and Back

Before I get into the heart of this post, I want to ask a leading question:

It only takes about forty minutes for me to commute to work in the morning.  Not a huge amount of time, right?  Certainly not compared to the whole rest of the day.  But one of the reasons that I take that specific route to work is that there are several places where I can stop to pee.

I’m sure it has something to do with the time.  That’s when the morning’s first cup of coffee has finished the processing cycle.  Or who knows.  All I know is, it’s a good thing that the route is mostly urban and not rural.

Which brings up another question:  If you’re just running in to use the facilities, do you take the time to lock up your bike and take the day pack with you?  You’ll easily spend twice as much time dealing with the bicycle than you will taking care of business.  Or do you trust that nobody will steal it in the two minutes it takes to run in and run out?

Which is all merely an awkward lead in into the story of last weekend’s ALC training ride.  We were supposed to meet in Menlo Park at 9:30, but I wanted to leave early just in case.  Jumped into the car at 8:30 and …

click click click click click click click…

No battery.  Damn.  Not gunna make it.

I know what you’re thinking.  A real cyclist would have abandoned the car and pedaled her way to Menlo Park.  First off: Never claimed to be a real cyclist.  Second: Didn’t matter, because it would still take longer than 90 minutes to get there.

After dealing with the battery, I was still itching to ride.

I fired up Google Maps and said, “Google, I need a bicycle route from the Tanforan Mall in San Bruno to Stanford University in Palo Alto.”

I’m impressed that Google did its algorithmic best to keep me off of large, busy streets.  But I found that this also slowed me down in the long run, mostly from having to stop every block at every suburban stop sign.  I spent more time shifting than pedaling.  I took a more direct route back, mostly along Highway 82, which is often the main boulevard through many of the towns along the way, and found that most of the cities along that route have added sharrows and even bicycle sensors for the signal lights.  There weren’t even any rude motorists to complain about.  Total distance for the day was just under 50 miles (49.75).

Here’s the kicker:  Many of the ALC training rides are a combination of cycling environments, including rural.  For some reason, my kidneys were working overtime.  Couldn’t blame it on the coffee.  This would have made the training ride embarrassing to say the least.

“Go ahead, guys!  I’ll catch up with you in a bit as soon as I’m finished with this bush.”

And looking at the 2012 route for the ALC, maybe I should be concerned.

Anybody else want to chime in on this?

The Technology of our Ancestors

Another recumbent rider who also blogs on WordPress recently wrote about the pros and cons of using ancient technology in preference to modern.  He makes a good point, and he was careful to moderate it with the phrase “a rule of thumb.”  He wrote, “I have developed a rule of thumb when evaluating if a health claim is true or not; If early humans did it, then it is good, otherwise it is bad.”

I didn’t want to instigate a long, drawn-out argument on his blog about this – mostly because I have no real argument – but I believe the subject does beg discussion, and this blog has been cooking in my mind for a couple of days now.

I have some of the same philosophies about life, though the rules are more complex.  I make every effort to buy local organic produce, for instance, and there are lots of farms here about, but coffee doesn’t grow in northern California, so there’s an exception right there.  And we aren’t giving up our computers.

Some of you know that I’m active in the Society for Creative Anachronisms, and that I have long studied the arts of the sword and the bow.  However, if a crazed rapist were to break into the house, you know I’d reach for the Smith & Wesson.  Even the most enthusiastic SCA-er will remind you that it’s “The middle ages as they should have been.”  Like, no Plague, we wear eye-glasses, and if you try to take away women’s suffrage, we’ll kill you with your own sword.

And, of course, there are some of us who simply wouldn’t be alive today if it wasn’t for 21st Century medicine.

So, can we agree that some modern solutions are better than bronze age ones?

Let’s take a closer look at some ancestral solutions, though.   The first question we have to ask is, “Which ancestors?”  The ones from pre-electric 19th century, or shall we go back as far as Australopithecus?  I’m not running around naked on the African savannah for anybody.  The original blog was about shoes, and the earliest known shoes are from bronze-age Mesopotamia.  That’s still a long ways to go back.

Difficult to pick, huh?

There is a popular television show on NBC called Revolution, and the major premise is that the entire world has been plunged into a permanent black out because all of the electricity has been turned off.  Remember that scene from The Day the Earth Stood Still? (The superb 1951 version, not the bastardized 2008 one.)  Well, it’s not 1951 anymore, and the consequences are even more dire.  Suddenly, we’re back to 19th Century agrarian communities.

Revolution is escapist post-apocalypse fantasy, though certainly not as much so as the book Dies the Fire (one of my absolute fave books, by the way!) Have you ever worked a farm using 19th Century technology?  I have.  It’s fun for about a week.  After that it’s just hard work, and lots of it.  And quite frankly, I don’t believe the current world’s population could be fed that way.

So, where do I stand on this issue?  Well, like almost everything else, it depends on the details.

More musings on this at another time.

Training for ALC-12 / Trejnado por ALC-12

In preparation for ALC-12


I have discovered that there is quite a sizable culture that has built up around the AIDS/LifeCycle ride.  Or ALC as the aficionados appear to prefer.

An invitation to participate in a training ride was posted to the Different Spokes – San Francisco message board by Terri Meier.  A 26-mile course of gentle terrain on a warm fall day on the San Francisco peninsula with a total climb of about 820 feet. I thought this would be a great way to meet some people. And I did get some training in how to ride with a group of ALC riders.

You can go to this page and see that there are training rides scheduled frequently, sorted by either the San Francisco area or the Los Angeles area. There are also training workshops. It’s obvious that the huge amount of planning which goes into this ride extends throughout the year, and is not simply concentrated in May and June.  The organization wants to make sure that not only do I get to L.A., but that I get there healthy and happy.

Upon arriving at the start of the October 28th training ride, introductions were made. Here I was introduced not only to the ride leaders, but also the veterans of the ALC who have made several trips.  Apparently, this event is addicting.

Nor was this a group of twenty-something, lean, overly adrenalinized athletic types.  Well, a few were.  Aside from all the Lycra, it looked like a group of people one might encounter on a random BART train.  All were friendly and welcoming to the noobs.

It needs to be mentioned that not a one of them pointed at my ‘bent and said, “Hey! It’s a lawn chair with wheels!”

Preparante por ALC-12


Eltrovis mi ke estas iome granda kulturo kiu kreskiĝis ĉirkaŭ la AIDS/Lifecycle rajdado. Aŭ ALC, kiel la amantaro ŝajne preferas.

Invito partopreni trejn-rajdadon, skribita de de Terri Meier, aperis ĉe  al Different Spokes – San Francisco afiŝejo. Ĝi estis 26 mejla vojo laŭ milda tereno dum varmeta aŭtuna tago ĉe la San Francisco duoninsulo kun totala grimpado de proksimume 250 metrojn. Kredis mi ke ĉi tio estus bonega metodo por renkonti aliajn rajdantojn.  Kaj mi akiris iom da trejnado en la maniero por rajdi kun grupo de ALC rajdantoj.

Vi povas iri al ĉi tiu paĝo kaj vidi ke estas trejn-rajdadoj ofte enhorarigitaj, ordigite laŭ la San Franciska aŭ la LosAnĝelesa lokoj. Ankaŭ estas trejnadaj studgrupoj. Estas evidenta ke la granda kvanto da planado por ĉi tiu rajdadp etendas tutjare, kaj ne simple estas koncentrita maje kaj junie. La organizaĵo volas certigi ke mi ne nur atingos la urbon L.A., sed ke mi alvenos sane kaj feliĉe.

Alveninte la komencon de la Oktobro 28a trejn-rajdado, enkondukoj estis farita. Tie ĉi mi estis enkondukita ne nur al la rajdgvidantoj, sed ankaŭ al la veteranoj de la ALC kiuj jam faris kelkajn vojojn. Ŝajne, ĉi tiu evento estas dependiga.

Ankaŭ ĉi tio ne estis grupo de dudekulaj, maldikaj, troadrenalinigitaj atletaj specoj.  Nu, kelkaj estis.  Krom la abondo da lycra, ĝi similis grupon ke oni povus renkonti sur hazarda BART-trajno. Ĉiuj estis amikemaj kaj bonvenigantaj al la novuloj.

Ĝi devas esti mencii ke ne unu el ili indikis mian kuŝbiciklon kaj diris, “Hej! Rigardu la gazonoseĝon kun radoj!”

Ride to End AIDS / Rajdado por Finigi Aidoson

Esperanto sekvas.


Yesterday, October 26th, 2012.  I signed up at AIDS/Lifecycle to participate in the 2013 ride.

This is a seven day, 545 mile (883 km) bicycle trip from San Francisco to Los Angeles.  Additionally, it’s a fundraiser in the fight against HIV/AIDS.

The information page will tell you that the trip “averages about 80 miles per day.”  Of course, what that doesn’t tell you is that the longest day is 109 miles, and the 40 mile day is full of hills with romantic names like “Evil Twin 1” and “Evil Twin 2.”  There are notations in the route sheet with ominous words like “Quadbuster!”

What amazes me is that I registered seven months before the event is scheduled to start, and I’m participant number 3361.

So on June 2, 2013, there will be a minimum of three thousand people gathered at the Cow Palace in San Francisco.  Not all of them will be cyclists.  But still.  How many more people will register between now and then?

The hard part is that I need to raise a minimum of US$3000 in pledges in order to participate.  That’s $420 a month between now and June.  Guess I’d better start saving my spare change.

I’ll be using the Haluzak recumbent, of course.  At least when I get to Los Angeles, I won’t have a sore butt.

Am I ready to do this ride?  Probably not.  But I will be in June!

Stay tuned for further details and stories of my preparation and a week on California highways.


Hieraŭ, je la 26a de Oktobro, 2012, mi registriĝis ĉe Aidoso/Vivciklo por partopreni la rajdadon de 2013.

Tio estas septaga, 545 mejlo (883 km) biciklado de San Francisko ĝis Los Anĝeleso.  Cetere, ĝi estas kvestilo por la batalo kontraŭ HIV/Aidoso.

La informpaĝo sciigas ke la vojaĝo “meznombre atingas ĉiutage 80 mejlojn.” Kompreneble, ĝi ne sciigas vin ke ke la plej longa tago havas 109 mejlojn (176 km), kaj la 40 mejla tago estas plena de montetoj kun romantikaj nomoj kiel “Diabla Ĝemelo 1” kaj “Diabla Ĝemelo 2.” Estas signaroj en la vojo-folio kun minacaj vortoj kiel “Quadbuster!”

Tio kio mirigas min estas ke mi registris sep monatojn antaŭ la evento okazos, kaj mi estas partoprenanto nombro 3361.

Nu, je la 2a de junio, 2013,  estos minimume tri mil homoj amasitaj ĉe la Cow Palace (Bovino Palaco) en San Francisko.  Ne ĉiuj estos biciklantoj.  Sed ankoraŭ. Kiom da pli homoj registros antaŭ tiam?

La malfacilaĵo estas tio, ke mi devas kvesti minimume US$3000 en promesoj por partopreni. Tio estas $420 monate inter nun kaj junio.  Konjektas mi, ke mi devas komenci savi la ŝparajn monerojn.

Kompreneble, mi uzos la kuŝbiciklon de Haluzak. Almenaŭ, kiam mi atingas LosAnĝeleson, mi ne havos doloran postaĵon.

Ĉu mi estas preta por ĉi tiu rajdo?  Verŝajne ne.  Tamen, ja en junio!

Pli da sciigoj sekvos.  Revenu por legi la historion pri mia preparado kaj la semajno sur la ŝoseoj de Kalifornio.