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Technical Q&A with Lennard Zinn – What’s the speed limit? Do the math

  • By VeloNews.com
  • Published Nov. 28, 2006

By Lennard Zinn

Bryan Lopes trying to hit sterminal at last year’s Red Bull Road Rage

Photo: Fred Dreier

Things to consider on a descent
Dear Lennard,
What speed can a standard road bike achieve? I know there are a lotof factors. I am a 125 lb. rider and my max is 56.8 mph on a long downhill.I am talking standard road-race bike and attire. At what speed will a standard bike and rider’s drag keep him from going any faster?It’s hard to word this but I think you know what I mean.
Chris

Dear Chris,
Yes, I can figure out what you are asking.When cycling, you must consider the forces of rolling resistance, airresistance and gravity, which when added together, give the power the riderputs out to maintain his or her speed, “s.” From DiPramperoet al., 1979 (sorry, I only found it in Portuguese), the equation lookslike this:

P = krMs + kaAsv2+ giMs
where P is power, kr is the rolling resistance coefficient,M is the combined mass of cyclist and bicycle, s is the bicycle speed onthe road, ka is the air resistance coefficient, A is the combinedfrontal area of cyclist and bicycle, v is the bicycle speed through theair (i.e. road speed plus head wind speed), g is the gravitational accelerationconstant, and i is the road incline (grade; however, this is only an approximation,as the sine of the road angle to the horizontal should technically be used).When you coast downhill, you are adding no power, so you reach terminalvelocity when the gravitational force pulling you down the hill equalsthe drag forces resisting your motion. So, terminal velocity is when:
krMs + kaAsv2 = giMs
When you are moving fast downhill, the aerodynamic drag forces are hugecompared to the rolling resistance forces, so you can ignore them. Andyou clearly want to know the answer in general, meaning on a calm day,rather than how fast you go into a headwind, so s = v, making the equationbecome:
kaAs3 = giMs
or
sterminal = (giM/kaA)1/2

Obviously, the heavier the rider and the steeper the hill, the biggerthe giM term becomes, and the bigger sterminal becomes. Similarly, thelower the frontal area, A, of the bike and rider, the higher the terminalvelocity becomes. This, of course, is the reason for tucking on your bikewhen you descend.An interesting thing that you can see from this terminal-velocity equationis that there is a terminal velocity beyond which you will not gounless you pedal or the hill becomes steeper. This means that you willget down the hill the fastest the sooner you get to terminal velocity.So it always pays to sprint over the top of the hill and the beginningof the descent before you go into your tuck. You will arrive at the bottomsooner than if you had simply gradually coasted up to sterminal.
Lennard

A spherical solution
Dear Lennard,
I just bought a Cervélo that is obviously carbon and is equippedwith a carbon post. It keeps slipping back into the frame and decreasingsaddle height. How can I fix this without over-torquing/breaking the seatpostbolt?
KeithDear Keith,
You need the new orange “assemblypaste” for carbon. Tacx has sold this in Europe for a few years, butnow both Ritchey and FSA sell it in the USA. It is like grease, but itis a paste containing millions of small plastic spheres. Unlike using anabrasive in a greasy suspension, like valve-grinding compound, or juststirring some sand in with grease (both of which often work in this kindof a case), the Ritchey/FSA/Tacx assembly paste won’t scratch the seatpost(or handlebar or whatever you are tightening). The little spheres pushback against the seat tube walls as hard as they are compressed, and theydon’t just squeeze out of the way as grease would.
LennardWhy can’t I solder it?
Dear Lennard,
I’m partial to soldered cable ends as a matter of preference.I recently got a new bike equipped with Campagnolo components, includingcables. I think the components are a few years old as the bike wasa gift from someone who didn’t ride it but let it sit in the garage.Nonetheless, the soldering technique I typically use on performance brandstainless cables would not work on the Campagnolo cables, and I am mystifiedas to why.I have soldered all kinds of things in the lab, including making vacuumtight joints on stainless steel, but no matter what I try I cannot makethe Campagnolo cables solder nicely. I have been cleaning with sandpaper,soap and water, acetone, and isopropyl, with out success. I’musing a bottle of flux that has worked for the generic cables. Thatsaid, the tips and the center of most Campy cables do seem to wet.I was wondering if there was a magic coating or oil thwarting my effortson Campy cables specifically. My understanding is that all stainlesssteels are solderable.
CorneliusDear Cornelius,
Stainless steel is solderable, yes. However, in the presence of grease,which is certainly deep inside those cables, the solder will not stick.Soldering flux alone may work as a pickling agent, but my experiences inteaching jewelry-making in college showed that no amount of flux or ofcleaning with the types of agents you list could clean oily, tightly-packedwire strands sufficiently to solder them. Pickling in a strong acid usuallydoes work, however, and that is the one agent you do not list. I wouldtry dunking that cable end in hydrochloric acid (HCl) first. I’m certainthat you can solder it then. We used to pickle jewelry parts to be solderedin an acid bath over a hot plate. Using hot acid was very effective, butI suspect the damage to our lungs was not worth it.Just a note to consider, Cornelius, Campagnolo does not use solderedcable ends any longer due to the toxicity of lead-based solder. Instead,electrowelding prevents the (uncut) cable end from fraying.
LennardFollow-up
Dear Lennard,
I had exact same problem with my Ultegra STI shifter as I read aboutin yourOctober 31 column. I found it was a kink or rough spot on theinside of the shifter cable not visible from the outside. I simplyexercised and reversed the cable housing and re-greased the cable and allwas fine. Would be worth Demian’s time to give it a try first.
CharlesDear Lennard,
This is regarding problem No.2 in the “a few problems” letter in your10/31 column. I have run into few bikes that exhibit exactly the symptomsthat Demian is describing. The problem often turns out to be a double cranksetpaired with a front derailleur made for a triple.
JeremiahDear Lennard,
Regarding your October 31 column – Problem 2: Is it possiblethe shop installed a triple BB for a double crank? This would pushthe chainline out far enough to cause this kind of thing.
LarryDear Lennard,
Like Demian, I had a problem shifting to smaller cogs with my Ultegra9s STI levers. It turns out that there is a small screw in the backof the inner shift lever that had worked its way out. Because ofthis, upshifts were soggy feeling, and didn’t always work. Replacingthe screw (I used a brake shoe fixing Allen screw off an old Ultegra brakeblock) fixed the problem.
StaceyDear Lennard,
I’m sure it’s not the same thing but this article filedOctober 18, 2006 called “Crunch time” from Debbie reminded me of aproblem I had last year. It sounds silly, but caused a lot of frustrationuntil I figured it out. My Campy 10-sp rear shifter would periodicallylock-up, and not shift into the larger gears. It would still shift intosmaller ones, and after several attempts would ultimately start shiftingperfectly again. The sporadic nature of the problem meant I was alwaystrying to trouble-shoot in the middle of a ride (usually while trying notto fall off the bike, because I couldn’t get a small enough gear to keepclimbing while riding). At any rate, the problem turned out to bethe brake hood. It wasn’t quite centered, and would get jammed up insidein the bottom of the lever, where you couldn’t see it. Straightened outthe brake hood, and no problems since.
ArthurDear Lennard,
You said in your10/18 column on “Coming up to Speed” that “If you switch the indexgear and ratchet ring to a 9-speed inside the right Ergo Power, it willshift fine with a 10-speed rear derailleur, and you can run a 9-speed chainjust fine, too.” I also prefer a 9-speed setup. However, BranfordBike says, “We recommend replacing the pulley wheels with wider, 8.8mmnine-speed ones, to accommodate 9 speed chains. We do not recommendusing 9 speed chains with 10 speed pulley wheels. The chain will hit theinside pulley wheel cage plates causing excess wear and noise. Tenspeed pulley wheels are 8.4 mm wide and have tiny “C10″ letters stampedon the steel end caps. Nine speed pulley wheels have plain end caps andare 8.8mm wide. The actual plastic toothed wheels are the same for 9- and10-speed; only the end caps and internal bushings are different.”What is your opinion on this?
StevenDear Steven,
Yes, that is a better solution than leaving the 10-speed derailleuras is when running it as a 9-speed.
Lennard


Technical writer Lennard Zinn is a frame builder (www.zinncycles.com),a former U.S. national team rider and author of several best-selling bookson bikes and bike maintenance including Zinn& the Art of Mountain Bike Maintenance, which is now availableas a 4-hour instructional DVDZinn& the Art of Road Bike Maintenance, and Zinn’s Cycling Primer:Maintenance Tips and Skill Building for Cyclists. Zinn’s regular columnis devoted to addressing readers’ technical questions about bikes, theircare and feeding and how we as riders can use them as comfortably and efficientlyas possible. Readers can send brief technical questions directlyto Zinn. Zinn’s column appears here each Tuesday.

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