A little boost math, psi->hp correlation

[DinK]

I was just playing with some numbers at work today, and I want to see if you guys think they fit. I was wondering how well crank hp output could be determined by air intake, or more specifically boost pressure.

Totally stock the engines run what, like 8 psi? Add that 8psi to the 14psi of normal atmospheric pressure to get 22psi overall. Multiply that by around 10, and you get 220hp. Sounds about right for a stock engine with some standard breathing mods.

Then, say you go "stage 1" and stay mostly stock on stuff like injectors. 15psi seems to be the recommended level without heavier fuel delivery. Add that 15 to the 14 and you get 29psi, times 10 again is 290hp. That's right around the 300 that this site's "stage 1" mods claim.

Doing the same math in reverse, to get 400hp you'd need 26psi of boost, for 40 = 26 + 14.


So, in your experience, does this seem at all accurate? I realize the boost numbers are usually peaks and it often goes down by the time you hit the end of the tach, but it still kinda makes sense that there's a linear air-hp relationship. After all, horsepower is energy per unit of time.

I'm not too sure about the 26psi = 400hp in particular. I don't have that much knowledge about these cars. Would be cool though, if 1 psi was roughly 10 horsepower, it would make power guesstimates rather easy. =)

 

[L2RTSiAWD]

1psi in a perfect world is 10hp.

 

[DinK]

Good to see somebody agrees. It seems pretty accurate for these cars, though not necessarily so for others.

A WRX runs near 12-14psi max I think, so that would put it at 260-280.

The EVO VIII I heard is like 19psi, so that's 330.

Still seems somewhat accurate, since in both cases you have modern emissions and stuff holding it back, plus in the DSM's case we're talking about other mods like intake and full exhaust.

 

[DrZiplok]

Given that horsepower is a function of torque and speed, not to mention the dozens of other problems with your math...

Bogus. Very bogus.

 

[95GST]

10hp / psi is a generalization! do you think a t-66 and a t-25 both make 10hp / psi..

 

[98TsiAWD]

Hp per PSI all depends on other conditions and mods. On a stock car however 1psi is ~5hp, but it varies on every car.

 

[InferiorWang]

i've heard 1psi by itself was worth 2-3 and i've heard 5-6. It's really different based on tons of other mods.

 

[DinK]

Originally posted by DrZiplok
Given that horsepower is a function of torque and speed, not to mention the dozens of other problems with your math...

Bogus. Very bogus.

Actually, horsepower is a function of torque and rpm. The change in boost causes a change in torque. More torque means more horsepower at the same revs. (but who's being picky, right?)

I also said that I was approximating and doing things in a very general way. It would be interesting, however, to find out how much horsepower is usually gained per PSI of boost, at least over a small range. I pulled the 10 number out of the air, and it seemed at least somewhat good.

I'd like to see where my "dozens" of math errors were though. I mean, 14 + 15 is still 29, right?

 

[JayHass]

Here is a post from the Nissan SE-R mailing list by Rob Cadle, who is an actual Garrett Engineer and does this sort of thing for a living.

>Here are the official #'s from the past weekends dyno.

>@10psi 271hp 244 lb/ft
>@14psi 323hp 293 lb/ft
>@20psi 392hp 367 lb/ft

If you want a good way to estimate horsepower on a turbo car, look at Ryan's
result and use this rule of thumb: Power is a function of airflow. Airflow
is a function of density. Density is a function of absolute pressure.

Let's see how it works. At 10 psi, manifold pressure is 24.7 psi absolute
(10 psi gauge plus 14.7 psi ambient pressure). At 14 psi, manifold pressure
is 28.7 psi absolute. Therefore, the power at 14 psi should be:

power = (28.7)/(24.7)*271 = 314.9 hp. That's a 2.5% error. Not bad
correlation

At 20 psi, manifold absolute pressure is 34.7 psi. Power should be:

power = (34.7)/(24.7)*271 = 380.7 hp. That's a 3% error. Not bad.

This assumes many things, of course, like 1) you don't run out of injector,
2) compressor and turbine efficiency is roughly constant, 3) intake manifold
temperature doesn't increase too much, 4) the turbo doesn't choke.

Have fun, turbo guys.

Rob

That should answer any question about how to do it.

 

[DinK]

Ah, very cool JayHass. It's interesting to read what somebody else has done with a real car.

The increase is definitely not going to be linear, but at a few percent error it's close enough for rough estimates.