Rich
> ----------
> From: Lawrence E. Mayfield[SMTP:mayfield(at)traveller.com]
> Reply To: Lawrence E. Mayfield
> Sent: Tuesday, March 10, 1998 8:27 AM
> To: alpines(at)autox.team.net
> Subject: Updated HP vs Speed
>
> About a month ago, I posted a couple of responses to a question asked by
> one of the Alpine listers. The question was "How much Horsepower do I need
> to go 130 mph?" (or something similar..). I have updated the analyses to
> revise the drag coefficient, coefficient of friction between the road and
> tire, and to add rolling resistance due to tire flex. I ask your
> forgiveness if the formatting turns out crappy...
>
> 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!"
>