Dr Palmer has shown, through his equations that I need somewhere around 1600
or 1700 horsepower to attain 260 or so miles per hour at Bonneville. The
following is part of the dissertation I posted some time back. Remember, I
started with the premise that rolling friction parameters were small effects
and were within the bounds of errors and assumptions and so did not include
them. Same holds true for the gravity component of going uphill because the
dry lakes and salt flats are, well, flat.
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. They are also in accordance with Thomas Gillespie's Text,
"Fundamentals of Vehicle Dynamics", a 1992 text from SAE.
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.
Plugging in the parameters:
V = 260 mph = 381.3 ft/sec (jeeze, one and a third football field every
second!)
Cd = 0.45 (my estimation of Tiger/Alpine drag coefficien)
S= 15 sq. ft.
Rho as given
we get
HP = (0.00238)(381.3)^3(0.45)(15)/1100 = 809.6 HP
for an approximate standard Sunbeam Tiger.
But, my car is minus the windshield, has the grill blanked off and has an air
dam to smooth the air flow. I figure the drag coefficient is reduced to
something around 0.35. This can be correlated to modern cars with Drag
coefficients of about 0.3. I think my frontal area is also reduced to
something around 13 sq ft. And I will be running at Bonneville where the
altitude is around 3500 ft (I think, my recollection is dim here!) which would
make the air density around 0.00213 for a standard day. However, August is not
a standard day and the density is reduced a little more. I just use 0.0021.
The error is small, I think. Oh, and for my engine airflow calculations is
also
reduced the density as input to the turbos for compensation.
Plugging in these numbers
V = 260 mph = 381.3 ft/sec
Cd = 0.35
S= 13 sq. ft.
Rho = 0.0021 slugs
we get
HP = (0.0021)(381.3)^3(0.35)(13)/1100 = 481.5 HP
for the conditions at Bonneville, including the reduced frontal area, and
reduced drag coefficient.
This would seem to indicate that 650 horsepower is more than enough. Just for
drill, I chatted with Doc Jefferies, of Bonneville fame (holder of 20 some od
records over the years) and his guestimation was that the horsepower should be
way more than enough. It is further interesting that some of the new breed
(read Asian foreign) cars wih dual turbos, and four cylinder engines have
reached well in excess of 200 mph.
I want to thank Dr. Bob for requiring me to recheck my numbers. I think they
are right. I think Dr. Bob forgot to divide by 2 (or did I?). In any case,
right wron,or indifferent, I am gonna try with what I believe is right. Time
will tell. Getting the horsepower will be the trick.
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