Technical aspects of road time trialing

Transcription

1 Technical aspects of road time trialing

2 Acknowledgements Andrew Coggan,, Ph.D. Kraig Willett, biketechreview.com cyclingnews.com North Chattanooga Cycle Club Excel Sports Cervélo HED Kestrel Litespeed Softride

3 Part I: THEORETlCAL CONSlDERAT DERATlONS

4 Speed, power, and force Speed is the quotient of power and force, or s = P / ΣF Therefore, to maximize speed, power must increase and/or resistive forces must be decreased: s = P / ΣF

5 Forces resisting forward motion of bicycle/rider system 1. air resistance (from body, bike, and wheels) 2. tire rolling resistance, from energy lost due to flexion (deformation) of tire casing and tube 3. direct resistance from weight (uphill terrain only) 4. mechanical friction: rolling (hubs) and drivetrain (chain wrap, derailleur pulleys, bottom bracket bearings, pedal bearings, rear hub bearings) 5. inertial resistance (from changes in kinetic energy, i.e., accelerations)

6 Forces resisting forward motion of bicycle/rider system ΣF = (R a + R t + R w + R f + R i ) where R a = air resistance (drag) R t = tire rolling resistance R w = direct resistance of weight (uphill terrain) R i = inertial resistance from changes in kinetic energy of system

7 Expanded motion equation for cycling power requirement P = ΣF s = s [ R a + ( R t + R w + R f ) + R i ] = s [k a s 2 + mg (k t cosθ + sinθ + k f s ) + ma ] P = power output of system (rider+ equipment) as thrust at rear wheel in Watts ΣF = total resistive force in Newtons s = ground speed in meters/second R a R t R w R f R i = aerodynamic drag = tire rolling resistance = direct resistance of weight = mechanical friction of hubs = inertial inertial resistance k a m g = aerodynamic drag constant of system in kg/m = total mass of system in kilograms = gravitational acceleration constant = meters/second 2 mg = weight of system in Newtons θ = angle of road surface k t = rolling resistance constant = k f = mechanical friction constant in s/m = a = acceleration of system in m/s 2

8 Relative distribution of resistive forces on an 80 kg bicycle/rider at 300 W (constant) on grades 0-12%.

9 R a = 4.08 lb (84%) R (0.44%) f = 0.02 lb (0.44%) ΣF = 4.85 lb R f = 0.02 lb R t = 0.37 lb (7.6%) R t = 0.37 lb (7.6%) Forces resisting rectilinear (i.e., forward) motion of a 185 lb rider/bicycle at 25 mph (242 W) on flat terrain with no wind. Arrow length reflects relative magnitude (font size not to scale).

10 Apportionment of resistive forces (rolling circuit course) An analysis by Kraig Willett found the following breakdown of energy requirements on a rolling circuit course (i.e., zero net elevation gain): 60% rider drag 8% wheel drag 8% frame drag 12% tire rolling resistance 8% bike/rider inertia 0.5% wheel inertia

11 Air resistance (drag) 1. air resistance R a = k a v 2, k a = ½C D Aρ 0.359P B /T 2. the drag constant k a is proportional to barometric pressure P B and temperature T; ; air density ρ is inversely proportional to altitude, i.e., the higher you go, the thinner the air gets and easier it is to move through 3. effective frontal area C D A of the bicycle/rider is the product of aerodynamic drag coefficient C D, and frontal area A 4. frontal area A is the size of the surface the bicycle/rider system pushes through the air as it moves forward. C D is a measure of how streamlined the system is, i.e., how smoothly air flows around it without swirling behind, and modifies A to give effective frontal area.

12 Air resistance (drag) 4. To understand C D, consider two riders of exactly the same size and position, where one is using a Cervélo P3, an aero helmet, shoe covers, etc., while the other has a standard round-tubed bicycle and a Pneumo helmet. Both wheelsets have 42 spokes total (24 rear/18 front), but the first has 58 mm deep-section rims, while the second has standard box-section rims. Although both riders present the same frontal area, the former will have a lower C D, incur less aerodynamic drag, and go faster at a given power output.

13 Equal Frontal Area Different Drag Coefficient Images biketechreview.com RIDER A C D = 0.9 A = 0.30 m 2 C D A = 0.27 m 2 RIDER B C D = 0.8 A = 0.30 m 2 C D A = 0.24 m 2 For a 70 kg rider averaging 235 W, this reduction in C D A will yield a time savings of ~67 seconds in a 20 km TT (flat-terrain, sea level, 66 F, calm air)

14 Air resistance (drag) 5. C D A is most accurately determined in a wind tunnel, but can be measured with a power meter, on a flat course in calm air. Most improvement, however, can be made simply through visual inspection. Frontal area only can be measured using digital photography, a reference diagram, and pixel-counting software. 6. As a rule of thumb, at 30 mph, a reduction of m 2 in C D A = 0.5 seconds/kilometer = 0.1 lbs. drag = 7 W

15 Field testing to determine C D A In conditions of calm air and flat terrain, at a constant speed: P R a = ΣF s = s (R a + R t + R w + R f + R i ) = P/s (R t + R f ) 0 0 R a = k a v 2 k a = ½C D Aρ 0 (0.359P B /T ) = C D AP B /T C D A = k a T / P B whereρ 0 = air density at sea level = 1.23 kg/m 3 P B T = barometric pressure in mmhg = temperature in Kelvin

16 60 minute power and aerodynamic drag data for selected riders Rider Date Height (m)/ Mass (kg) Avg. Power (W) C D A (m 2 ) C D A (m 2 ) Power/C D A (W/m 2 ) Avg. Speed (m/s) CB 9/6/ / MI 9/2/ / GO 4/27/ / FM 1/21/84 1,2 1.82/ AC / EW 1.68/ CP 1.74/ CH 6/26/ / CH (Rakes) 1.80/ CH (drops) 1.80/ CH (brake hoods) 1.80/ World Hour Record 2 elevation 2240 m 3 calculated from speed and power data 4 measured by wind-tunnel testing Values for C D estimated from body position and equipment, frontal area estimated from rider height and weight.

17 Turbulent flow In turbulent flow, the air streams on each side of the tube do not reattach behind the tube, causing the air to swirl. This creates low pressure behind, and higher pressure ahead of the tube as the air in front is compressed. Laminar (layered) flow In laminar flow, air streams re-attach behind the tube, relieving pressure in front and allowing it to move through the air more easily at a given speed than the round tube, even though both have the same frontal area.

18 Effect of drag coefficient (C D ) on air resistance High C D (~1.0) Low C D (~0.1) Each tube has the same frontal area, but the lower C D is, the more laminar the air flow is, and the less drag it has.

19 Importance of leading edge To minimize aerodynamic drag, the leading edge must be elliptical, not round.

20 So just what is aerodynamic tubing? Are any of these tubes truly aerodynamic?

21 And which has the better profile? FSA VisionTech Easton Delta Force