I receive a bad mail message. So hee it is again, maybe...
>Date: Sat, 21 Feb 1998 19:10:34
>To: alpines(at)autox.team.net
>From: "Lawrence E. Mayfield" <mayfield(at)traveller.com>
>Subject: Horsepower vs Road Speed
>
>Someone, in the last few days, had asked about horsepower vs road speed.
Since I am an old (stress "old") aero engineer, I thought I would take a
stab at it. There is a very simple formula for calculating horsepower as a
function of forward velocity. Forgive me if the "formatting" does not come
out quite right on the screen. The equations come from "Airplane
Aerodynamics" published in 1961, para 6:8.
>
>HP = (Drag)(Velocity)/550
>
>Drag = (Rho)( V*V)(Cd)(S)/2
> Units of pounds (lb)
>or
>
>HP = (Rho)(V*V*V)(Cd)(S)/1100
> where Rho is Std Air Density (0.00237691999 Slugs/cu.ft.)
> V is velocity in ft/sec
> Cd is drag coefficient
> S is frontal area in sq ft.
>
>Several things are apparent: Horsepower needed is a function of the cube
of the forward
>velocity, Cd is probably hard to determine, but estimable, and S can be
grossly figured from knowing the dimensions of the car. Also, this is rear
wheel at the ground horsepower, not flywheel horsepower. Since our cars are
pretty slippery looking with the down sloped hood, rounded under valance,
and of course fins. The "S" in the equation is calculated to be about 18
sq ft. using dimensions from "Tiger An Exceptional Motorcar". One thing you
will have noticed is the absense or rolling friction. We will cover that a
little later (it is pretty small). In the referenced old text book (yeah, I
kept them all) is a figure, figure 6:3 which has several shapes and the
drag coefficient at very low Mach numbers. As a SWAG I selected one which
ia a cross between one that looks a little like a 45 cal slug (0.295) and a
bass ackward wedge (1.14) giving me a drag
>coefficient of 0.5. Why did I select this one? Just because. So, now
everything is known and it is a simple matter to work the equation. I use
Excel 4.0. Of course you can play with the equation and use various Cd, S
and air densities to see how you fare in your neck of the woods. Note that
Cd varies from a worst of 1.28 (flat plate normal to the wind) to .01 type
numbers for really slick shapes (not our beamers, tho). Also bear in mind
that this is for straight and level cruising, no climb, no acceleration.
Just what it takes to get you down the road. As you can see, the horsepower
to keep you moving is pretty small. And you can see the effects of
increased speed on fuel economy: as speed increases, fuel consumption
increases cubically. The effects of rolling
>friction from the rear axle bearings can be calculated in a similar
fashion but will add only small horsepower requirements. Excessive
toe-in/out causes drag also. Even if you estimate the rolling friction and
toe-in to be as much as 10 percent, it is still a small amount of
horsepower. The table below only factors wind resistance. The mechanical
efficiency to the flywheel might be 70% so just divide the numbers below by
0.70 to get an estimate of SAE horsepower (engine dyno) power needed.
>
>A better question might have been: "How much horsepower to accelerate to
driving speeds in X seconds?" This is not much harder to do and it involves
Sir Isaac Newton's equation: F = m a and some derived equations. Shall I
do it?
>
> Table 1
> Horsepower
>Vel (mph) Sea Level 2000 ft 4000ft
> 5 0.007675 0.007236 0.00681
>10 0.06 0.06 0.05
>15 0.21 0.20 0.18
>20 0.49 0.46 0.44
>25 0.96 0.90 0.85
>30 1.66 1.56 1.47
>35 2.63 2.48 2.34
>40 3.93 3.70 3.49
>45 5.60 5.27 4.96
>50 7.68 7.24 6.81
>55 10.22 9.63 9.06
>60 13.26 12.50 11.77
>65 16.86 15.90 14.96
>70 21.06 19.85 18.69
>75 25.90 24.42 22.98
>80 31.44 29.64 27.89
>85 37.71 35.55 33.46
>90 44.76 42.20 39.71
>100 61.40 57.88 54.48
>110 81.72 77.04 72.51
>120 106.10 100.02 94.14
>130 134.90 127.17 119.69
>
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!"
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