
Wayne Pein wpein@nc.rr.com February 2004 Revised July 2007 Figure 16. Braking from high speed on a descent takes considerable distance. Braking Performance According to AASHTO’s “Green Book,”A Policy on Geometric Design of Highways and Streets, in roadway design, braking and sight distance calculations for all vehicles, including bicycles, are figured using a deceleration rate of 3.4 m/s2 (11.2 ft/s2), which is 0.35 g. Fourwheeled motor vehicles have much better emergency braking capabilities than bicycles, approximately 0.6  0.7 g (some cars can achieve more than 0.9 g), affording motorists a great margin for error beyond AASHTO’s roadway design specification. In contrast, a typical bicyclist can be expected to decelerate at 0.35 g on clean, dry, level pavement which, coincidentally, is AASHTO’s figure for roadway design purposes as previously noted. A conventional bicycle's theoretical maximum deceleration is limited to about 0.6 g on level pavement by weight transfer, which can cause pitchover. However, only a highly skilled bicyclist using optimal technique may be able to achieve this 0.6 g; most will be far lower at about 0.35 g. For nonlevel roads the grade is added (+ or ) to this deceleration rate in gees. This means that on a 5% descent, for example, braking effort equivalent to 0.05 g is used to counteract the effect of gravity, leaving typical bicyclists only 0.35  0.05 = 0.30 g for deceleration. Further, unlike motor vehicle braking which is not markedly affected in wet conditions, the braking capability of some bicycles is greatly reduced due to the diminished friction between the brake shoes and a wet rim. According to John Forester [personal communication, 12/22/04] “Bicycle braking under wet conditions needs to be considered in two phases. The first phase is wiping the rims clean, the second phase is actual braking. For aluminum rims, one can consider three rotations of the wheel to wipe the rim reasonably dry. That is about 21 feet for typical wheel sizes. Subsequent braking, given good brakes to start with, is then typical of dry, unless the road surface is so slippery that it will not produce a 0.67 coefficient of friction. The situation with chromeplated steel rims is worse; they don't wipe dry.” At 20 mph (29 ft/s), 21 feet of nearly nonexistent braking adds about 0.7 seconds to braking time. Thus, instead of taking 2.6 seconds to come to a complete stop, it would take 3.3 seconds on level ground when wet, amounting to an average deceleration of 0.28 g. Heavy rain or road splash at high speed could result in continuously wet rims, further drastically reducing braking capacity. For sighttriangle and other operational calculations, bicycle deceleration rate in wet conditions should be considered to be slightly more than half that under dry conditions; 0.20 g. Moreover, BL stripes are very slippery when wet, adding an unnecessary longitudinal hazard. These concerns amplify the argument that BLs are counterindicated, especially on high speed descents. References AASHTO. Guide for the Development of Bicycle Facilities. 1999 http://www.johnforester.com/Articles/Safety/Cross01.htm Forester, John. Appendix A. Personal communication, December 2004. National Agenda for Motorcycle Safety website hosted by the National Highway Traffic Safety Administration (NHTSA). Appendix A John Forester, M.S., P.E. Cycling Transportation Engineer Consulting Engineer, Expert Witness & Educator in Effective Cycling, Bicycles, Highways & Bikeways, Traffic Laws 7585 Church St., Lemon Grove, CA 919452306 6196445481 forester@johnforester.com Www.johnforester.com November 25, 2000 NOTES ON RESISTANCE AND POWER IN CYCLING The standard model for calculating the resistance to motion of bicycles, using pounds, feet, and seconds, is: Resistance (lbs) = Slope Resistance + Rolling Resistance + Air Resistance Slope Resistance =Mass * Slope Rolling Resistance =Bearing Friction + Tire Losses (both empirically determined) Air Resistance =Density of air/2 * Cross Sectional Area * Drag Factor * Speed * Speed The accepted standard density of air at sea level is 0.002378 slugs/cu.ft. (Which equals 0.07657 lbs/cu.ft) The FHWA research done in Davis (FHWARD75112) gives the following resistances when using a system that uses pounds and hours and mixes feet with miles: Resistance, lbs (FHWA) =Weight*Slope + Weight*(0.005 + 0.15/TirePressure) + 0.00256*(AirSpeed*AirSpeed*DragArea* DragFactor) The 0.00256 factor converts the 0.002378 by combining the division by 2 and the conversion from feet per second to miles per hour. Also, their values for bearing and tire friction are high relative to what is available today. Good wiredon tires have improved greatly since then. The CycSpeed program reflects this change by using bearing friction of 0.002 and tire losses as 0.10/TirePressure. Whitt and Wilson give the following for typical drag areas and factors: Cyclist on roadster bicycle: 5.3 Square Feet and 1.2 Drag Factor Cyclist on sporting bicycle: 4.3 Square Feet and 1.0 Drag Factor Cyclist on racing bicycle: 3.55 Square Feet and 0.9 Drag Factor The resistance to acceleration (inertia) is greater than the mass by an amount very nearly equal to the mass of the tirs and rims. CycSpeed adds in the masses of the tires and rims. Whitt & Wilson call this the WheelResistanceFactor and typically give it a value of 0.01 for all bicycles. Whitt & Wilson give the following for resistance using metric (MKS) system: Res (newtons) = Mg(Rolling Resistance + Slope Resistance + Wheel Resistance Factor) + 0.5*(Drag Factor*Drag Area*Air Density*Airspeed*Airspeed) =Mg*(Cr + slope + a/g*1.01) + 0.5*Cd*A*R*(Vc + Vw)*(Vc + Vw) =Mg*(Cr + slope + a/g*1.01) + 0.5*1.0*0.4*1.226*V*V =K1 + K2V*V +10.32M(slope +a/g*1.01) Where K1 and K2 are per the following: K1 K2 Roadster bicycle 7.845 0.3872 Sports bicycle 3.509 0.2581 Racing bicycle 2.508 0.1916 John Forester, M.S., P.E. 

