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# BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

## BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

(OP)
I have a 1995 Ferrari F355. The published crankshaft power rating and published top speed are 375hp and 183mph, respectively. I wish to estimate the horsepower needed at 70mph and thereby estimate the BSFC at that cruising speed, at which the car gets 22mpg.

I made the assumption that power is proportional to velocity^3. This is based on the idea that drag force = 0.5(Cd)(velocity)^2, and that power = force*distance/time, which makes power proportional to velocity^3, if I did my analysis correctly. A further assumption is that other parasitic losses are also proportional to velocity^3.

The engine is turning about 200rpm over the rpm for rated power (around 8300) at the top speed. I assumed a crank hp of 370 for these conditions. Scaling back to 70mph this gives about 21hp at 70mph. This seemed reasonable, if even a little bit high for this car. This is all assuming a level road with no head wind of course.

With 21hp and 22mpg I get a BSFC of around 0.9 lbs/hp/hr, which seems really high. I realize these are part throttle conditions but it still seems high. Any thoughts?

### RE: BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

Sounds pretty reasonable I think, this engine is not tuned for fuel economy. Certainly within the ball park given all the assumptions.

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### RE: BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

FWIW isn't the EPA rating something like 20 mpg highway, which I'd expect to be under more economical conditions than 70 mph.

So about 3200 rpm at 70 mph? 22 mph/1000. Hardly economy gearing, at least for more mundane vehicles to be sure.

the engine is at about 25% load under the cruising condition you described, if this synthesized power curve is correct,
\http://www.automobile-catalog.com/wykres_power.php

here is a BSFC chart allegedly from a high revving NA engine ( Honda S2000 ).\
http://i273.photobucket.com/albums/jj229/MarquisRe...

looks like it is pretty possible to halve the best BSFC at low throttle settings at 3200 rpm

### RE: BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

21 hp sounds about right, perhaps a little low, at 70 mph.

I can't imagine Ferrari gave two hoots about part load fuel consumption.

Cheers

Greg Locock

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### RE: BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

If you're lucky, by searching you might be able to find the actual road load coefficients for your vehicle. These are generally published in order to facilitate CARB/EPA chassis dyno testing. For background info, see SAE J1263. There is a related standard, which translates the road load measurements to the chassis test procedure. The point is, the drag curve of your vehicle has already been accurately measured, so if you find it you can get a more accurate estimate of the road load at 70mph.
You can also follow the procedure in SAE J1263 and determine the drag curve yourself, but this is not a trivial task.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

### RE: BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

You are right - 0.9 lb/hp.hr (about 550 g/kW.hr) is pretty high.

By assuming a V^3 coefficient, you will underestimate the road load at 70 mph. The V^1 and V^2 terms in the polynomial obviously do not drop off as quickly as the V^3 term as you reduce speed from 183 mph to 70 mph.

je suis charlie

### RE: BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

#### Quote (gruntguru)

By assuming a V^3 coefficient, you will underestimate the road load at 70 mph. The V^1 and V^2 terms in the polynomial obviously do not drop off as quickly as the V^3 term as you reduce speed from 183 mph to 70 mph.
This.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

### RE: BSFC at cruising speed in a car from power=kspeed^3 to estimate horsepower?

(OP)
I guessed you missed this statement in my original post :)

A further assumption is that other parasitic losses are also proportional to velocity^3.

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