Remember...
HP = (Drag)*(Velocity)/550 + Wheel Bearing Loss (HP)
Wheel Bearing Loss (HP) = Mt * N /63000 where: Mt = F * f * D * N F = Bearing Radial Load (lbs) = 600 lbs f = Friction Factor = 0.0018 D = Bearing Bore (inches) = 1.125 inches N = RPM = (Velocity - ft/sec)*(60 - sec/min) / (pi * tire dia (ft)) = 9.55 * Velocity
Drag is the sum of all forces acting in opposition to forward motion. In the previous analyses, I had considered aerodynamic drag and tire side slip (from toe in/out). Now I have included tire rolling resistance due to pressure and road surface (25 psig and smooth concrete). Here goes...
Drag = Aero + Tireslip + Rolling Resistance
Aero = (Rho)(V*V)(Cd)(S)/2 where: Rho = Std Air Densities (sea level = 0.002377 slugs/ cu. ft 2000 ft = 0.002241 " " 4000 ft = 0.002109 " " V = Velocity in ft/sec Cd = Drag Coefficient = 0.45 ( was 0.50) S = Alpine Frontal Area (sq ft) = 18 sq ft (est.)
Tireslip = (Mu) * P * sin(slip angle) * 2 where: Mu = Coefficient of friction, rubber - road = 0.62 (was 0.50) P = Weight on One Front Tire (lbs) = 600 lbs Slip Angle = ARCTAN(Toe in/out / contact patch length) = ARCTAN(0.125/6) = 1.2 degrees
Rolling Resistance = fr * W where: fr = resistance coefficient = fo + 3.24 *fs* (Sp/100)^2.5 Sp = Speed (mph) fo = Basic Coefficient = 0.012 (From ref 2 at 25 psig) fs = Speed Effect Coefficient = 0.0076 (From ref 2 at 25 psig) W = Vehicle Weight = 2400 lbs
Putting it all together and plugging in the numbers to get...
HP = (600)*(0.0018)*(1.125)*(V)*(9.55)/63000 (Wheel Bearings) + (0.002377)*(V*V*V)*(0.45)*(18)/1100 (Aerodynamics) + (0.62)*(600)*(sin(1.2))*(2)*(V)/550 (Tire Slip) + ((0.012 + 3.24 *(0.0076)*((V)*1.467/100)^2.5) *2400)*V/550 (Rolling Res)
Which reduces to
HP = 0.0001842*V + 0.0000175*V^3 + 0.028*V + (0.052 + 0.011*(.007*V)^2.5)*V
Plugging that into Excel 4.0 and varying the second term (density) and find the data in Table 1!
Table 1 Speed Vel. HP HP HP (mph) (ft/sec) (s/l) (2000') (4000') 5 7.34 0.60 0.59 0.59 10 14.67 1.23 1.23 1.23 15 22.01 1.95 1.94 1.93 20 29.34 2.80 2.78 2.75 25 36.68 3.82 3.77 3.72 30 44.01 5.05 4.96 4.88 35 51.35 6.53 6.39 6.26 40 58.68 8.31 8.11 7.91 45 66.02 10.43 10.15 9.87 50 73.35 12.94 12.55 12.16 55 80.69 15.87 15.35 14.84 60 88.02 19.28 18.60 17.94 65 95.36 23.20 22.33 21.49 70 102.69 27.68 26.60 25.55 75 110.03 32.76 31.43 30.14 80 117.36 38.49 36.87 35.30 85 124.70 44.91 42.97 41.09 90 132.03 52.06 49.75 47.52 95 139.37 59.99 57.28 54.65 100 146.70 68.74 65.58 62.52 105 154.04 78.35 74.70 71.16 110 161.37 88.88 84.68 80.61 115 168.71 100.37 95.57 90.91 120 176.04 112.85 107.40 102.10 125 183.38 126.38 120.21 114.23 130 190.71 140.99 134.06 127.33 135 198.05 156.74 148.98 141.44 140 205.38 173.67 165.01 156.61 145 212.72 191.82 182.20 172.86 150 220.05 211.24 200.58 190.25 155 227.39 231.97 220.21 208.81 160 234.72 254.06 241.13 228.58 170 249.39 302.48 286.97 271.93 175 256.73 328.91 311.99 295.58 180 264.06 356.88 338.47 320.61 185 271.40 386.43 366.44 347.05 190 278.73 417.61 395.95 374.95 195 286.07 450.46 427.05 404.34 200 293.40 485.03 459.77 435.28
L.E. Mayfield 124 Maximillion Drive Madison, Al. 35758-8171 205-837-1051
DrMayf(at)AOL.com mayfield(at)traveller.com <<<<preferred
"Thought is the software of the mind; rational thought is bug free!"