In January, 1998, 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(B) * 2 
     where: Mu = Coefficient of friction, rubber - road = 0.62 (was 0.50) 
             P = Weight on One Front Tire (lbs) = 600 lbs 
             B = ARCTAN(Toe in/out / contact patch length) (B is slip angle) 
               = 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 
            fs = Speed Effect Coefficient = 0.0076 
             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 and plotted in Figure 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	18.60	17.94	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