Calc max available HP% by altitude

[AA5Bman]

I feel like I know - or should know - the answer to this question, but how would you go about calculating the maximum available horsepower for a normally aspirated engine at a given (density) altitude?

I’m curious about calculating the crossover point or altitude where a smaller turbocharged engine is more powerful than a larger NA engine, and I can’t quite remember how to do so!

 

[GeorgeC]

IIRC, 3% loss per 1000 feet in altitude?

 

[AA5Bman]

IIRC, 3% loss per 1000 feet in altitude?

I’ve seen that number, but it’s just a rule of thumb. I assume there’s a way to calculate this directly?

 

[RyanB]

Yeah, 3% loss / thousand feet is a rough rule of thumb. We know that elevation and density altitude has the same effect, so try this basic formula that I was taught.

HP Lost= Elevation x 0.03 x hp @ sea level/1000

So in my case, I’m at 690ft.

HP lost = 690 x 0.03 x 160/1000 = 3.312

160-3.31 = 156.6bhp available. Input the required variables for your airports elevation and rated hp by your engine.

 

[GeorgeC]

I don't know about calculating them from first principles, but you can look up the answers in the charts in the engine manuals.

 

[Clip4]

I feel like I know - or should know - the answer to this question, but how would you go about calculating the maximum available horsepower for a normally aspirated engine at a given (density) altitude?

I’m curious about calculating the crossover point or altitude where a smaller turbocharged engine is more powerful than a larger NA engine, and I can’t quite remember how to do so!

The difficulty is the curve is not linear.

 

[Palmpilot]

The difficulty is the curve is not linear.

Which is supported by the fact that the linear formula above says you lose 105% of your horsepower at 35,000 feet.

 

[PeterNSteinmetz]

The max power available should be proportional to air pressure since the max power will be achieved at the stoichiometric ratio for fuel/oxygen. This given that the fraction of oxygen isn’t changing much with height in the troposphere and assuming proper leaning.

So about 1 inch of Hg pressure per 1000’ is just about 1/30 ~ 3% near sea level as given in a prior post. If you want to be a bit more accurate, use a better formula for pressure as a function of altitude, but I believe the linear approximation is usually used at altitudes where normally aspirated engines are usually flown.

There is a graph and are more accurate formulas in the Wikipedia article at https://en.m.wikipedia.org/wiki/Barometric_formula

 

[Palmpilot]

This calculator requires entry of four variables, temperature, barometric pressure, relative humidity, and altitude:

http://www.csgnetwork.com/relhumhpcalc.html

 

[asicer]

Which is supported by the fact that the linear formula above says you lose 105% of your horsepower at 35,000 feet.

I'd like to see you fly a NA airplane that high to prove it wrong.

 

[Palmpilot]

I'd like to see you fly a NA airplane that high to prove it wrong.

Carry the NA engine aloft in an unpressurized jet and see if it still runs at 35,000 feet!

 

[RussR]

As an example, one day I was flying in a PA-32, fixed gear, 300 hp turbo model, along the same route as a friend in a Commander 114, 260 hp, normally-aspirated retractable. So, I had more power, he had less drag. At 6500 MSL we were almost exactly equivalent on airspeed at whatever power settings we were each running. I was a few miles behind him and staying there.

Due to wind, we decided to climb to 8500. When we got there, at the same power settings, I was now gaining on him at a few knots, maybe 5. That's almost solely due to the turbo being able to maintain power at 8500 while his airplane wasn't able to.

It was an interesting unplanned experiment.

 

[PeterNSteinmetz]

Just for fun here are two plots. The first is the pressure as a function of altitude for both the more accurate formula and the linear approximation. The second is the percent error in the linear approximation as a function of altitude. Reaches 5% at about 12,000 feet.

 

[AA5Bman]

Interesting. Just so I understand, in the first chart the red line is the loss in available power calculated using the 3% rule of thumb, and the black line is the actual, non-linear calculation. The second chart just plots the difference (in %) between the two. Is that right?

It looks like down low the NA engine performs worse than the 3% ROT, but after a bit over 5,000’, it performs a little better than the ROT (which makes sense because 3% would be trying to take the “average” decay over a segment of a curve), but in either case isn’t much of a difference in the sub-teens altitudes.

The operative altitude here is density altitude, right? Only other contender seems to be pressure altitude, but I’m thinking DA.

 

[PeterNSteinmetz]

These are just graphs of the predicted pressure, using both the 3% rule and the more accurate rule, as a function of height above MSL in the standard atmosphere. So if the temperature is standard, then I think the performance should be proportional to the pressure if the engine is leaned properly. If you go to the height corresponding a given density altitude, I think that should give engine performance for that DA fairly well.

 

[Salty]

Just remember that the entire time before you get to where the two HP curves finally meet, you've got less power with the turbo. You can get to that altitude a whole lot quicker and safer with the larger NA engine. Unless you're flying almost all your time in high altitudes, you want the HP over the turbo. Heck, even then you want the the HP, you just want the turbo also.

 

[Skip Miller]

I'd like to see you fly a NA airplane that high to prove it wrong.

Piston powered planes can do this. The #1 place goes to the B-29 mentioned below, and #2 place goes to Bruce Bohannon. From Wikipedia:

Flying from his home airport in Angleton, Texas, Bohannon flew his by now world-renowned, highly modified RV-4 to an altitude of 47,530 feet - just 380 feet lower than the all-time U.S. piston altitude record of 47,910 set in 1946 by a U.S. Air Force B-29.

 

[GRG55]

Just remember that the entire time before you get to where the two HP curves finally meet, you've got less power with the turbo. You can get to that altitude a whole lot quicker and safer with the larger NA engine. Unless you're flying almost all your time in high altitudes, you want the HP over the turbo. Heck, even then you want the the HP, you just want the turbo also.

"There's no substitute for cubic inches"

 

[wrbix]

"There's no substitute for cubic inches"

There’s no replacement for displacement

 

[AA5Bman]

Just remember that the entire time before you get to where the two HP curves finally meet, you've got less power with the turbo. You can get to that altitude a whole lot quicker and safer with the larger NA engine. Unless you're flying almost all your time in high altitudes, you want the HP over the turbo. Heck, even then you want the the HP, you just want the turbo also.

The crossover point for the two engines I’m considering is at about 4,500 which is less than our typical field elevations, so while technically true... this is for considering adding a turbo (supercharger) to a 260 hp IO-470 vs. replacing it a 300 horsepower NA IO-550.

 

[asicer]

Piston powered planes can do this. The #1 place goes to the B-29 mentioned below, and #2 place goes to Bruce Bohannon. From Wikipedia:

B-29 is supercharged and Bohannon's RV-4 was running on nitrous oxide. I wouldn't consider those to be NA (naturally aspirated).

 

[flyingron]

The max power available should be proportional to air pressure since the max power will be achieved at the stoichiometric ratio for fuel/oxygen.

Density, not pressure.

This given that the fraction of oxygen isn’t changing much with height in the troposphere and assuming proper leaning.

The fraction of oxygen isn't changing no matter what you do with the mixture control.

 

[flyingcheesehead]

I feel like I know - or should know - the answer to this question, but how would you go about calculating the maximum available horsepower for a normally aspirated engine at a given (density) altitude?

Here's the standard atmosphere up to 40,000 feet:



Look at the pressure ratio column, and that's about the max percent power you'll be able to get at that altitude. A normally aspirated plane can, thus, make 75% power up to 7000 feet and change, or 65% power up to 11,000 and change.

I’m curious about calculating the crossover point or altitude where a smaller turbocharged engine is more powerful than a larger NA engine, and I can’t quite remember how to do so!

Engines that are the same size and HP, the "crossover" is at sea level. Climb at all, and the NA one will start to lose some power while the turbo one will be able to maintain 100% power up to its critical altitude, after which it will start to taper off as well.

When you're speaking of smaller turbocharged vs bigger NA, the plane that comes immediately to mind is the Dakota. The NA version is a 235hp Lycoming O-540 while the turbo version is a 200hp Continental TSIO-360. If we assume that the crossover point is below the Conti's critical altitude, we just need to know where the Lyc will be developing 200hp. 200/235 = .8511, so looking at the chart, somewhere around 4400 feet.

However, if you're talking about cruise at 65% for example, the Conti will make .65*200 = 130hp at 65%. 130hp is .5532 * 235, so the NA version could cruise with that much power at about 15,500.

Now, these calculations aren't perfect. MP will drop a little more due to the air filter and possibly other intake quirks, mag timing may no longer be optimum, and plenty of other caveats. But, this is a start.

What *exactly* are you trying to figure out? What airframe(s), what engines? We might be able to give you a more accurate answer with additional information.

 

[AA5Bman]

Here's the standard atmosphere up to 40,000 feet:

View attachment 77717

Look at the pressure ratio column, and that's about the max percent power you'll be able to get at that altitude. A normally aspirated plane can, thus, make 75% power up to 7000 feet and change, or 65% power up to 11,000 and change.



Engines that are the same size and HP, the "crossover" is at sea level. Climb at all, and the NA one will start to lose some power while the turbo one will be able to maintain 100% power up to its critical altitude, after which it will start to taper off as well.

When you're speaking of smaller turbocharged vs bigger NA, the plane that comes immediately to mind is the Dakota. The NA version is a 235hp Lycoming O-540 while the turbo version is a 200hp Continental TSIO-360. If we assume that the crossover point is below the Conti's critical altitude, we just need to know where the Lyc will be developing 200hp. 200/235 = .8511, so looking at the chart, somewhere around 4400 feet.

However, if you're talking about cruise at 65% for example, the Conti will make .65*200 = 130hp at 65%. 130hp is .5532 * 235, so the NA version could cruise with that much power at about 15,500.

Now, these calculations aren't perfect. MP will drop a little more due to the air filter and possibly other intake quirks, mag timing may no longer be optimum, and plenty of other caveats. But, this is a start.

What *exactly* are you trying to figure out? What airframe(s), what engines? We might be able to give you a more accurate answer with additional information.

Thanks for this, good stuff.

I’m comparing putting a FAT supercharger on my existing 260 hp IO-470 vs swapping the engine with a NA 300hp IO-550. Both are extremely expensive so this is a thought experiment as much as anything for the moment. As far as I can tell, the supercharged IO-470 produces more horsepower after about 4,500’ which is meaningful for me as most of our field elevations are around 5,000’ + summertime DA. You make an interesting point about the differences between 65% power cruise, but in my application I’m mostly concerned with takeoff and climb performance anyway, and the stock IO-470 does fine in the cruise department as it is. Not really here to debate the merits of the FAT system - I know they’re kind of unproven - however I would be interested in hearing from anyone who *actually* has experience with them.

 

[flyingcheesehead]

I’m comparing putting a FAT supercharger on my existing 260 hp IO-470 vs swapping the engine with a NA 300hp IO-550.

Ah, cool! I followed their development on the supercharger for the DA40 but I don't know much about their other products. Which airframe?

With the Diamond one, they ended up optimizing the supercharger for ~12,000 feet because Diamond wouldn't cough up the engineering data to allow FAT to increase the ceiling of the plane from the existing 16,300 feet (5000m IIRC), so there was no sense in making it to allow a higher cruise than that.

I think they do tend to "supernormalize" rather than supercharge though, so you basically put the throttle up partway on takeoff, to get about 30" MP. As you climb, you continue increasing the throttle to maintain 30"MP until you're at full throttle which happens at the critical altitude.

It's worth asking FAT for the documentation on the system for your particular aircraft type to see what it'll get you.

Hopefully there's at least a couple of FAT supercharger owners here... They certainly don't seem to be too common, but from what I can tell it's a really nicely done system.

 

[AA5Bman]

Ah, cool! I followed their development on the supercharger for the DA40 but I don't know much about their other products. Which airframe?

With the Diamond one, they ended up optimizing the supercharger for ~12,000 feet because Diamond wouldn't cough up the engineering data to allow FAT to increase the ceiling of the plane from the existing 16,300 feet (5000m IIRC), so there was no sense in making it to allow a higher cruise than that.

I think they do tend to "supernormalize" rather than supercharge though, so you basically put the throttle up partway on takeoff, to get about 30" MP. As you climb, you continue increasing the throttle to maintain 30"MP until you're at full throttle which happens at the critical altitude.

It's worth asking FAT for the documentation on the system for your particular aircraft type to see what it'll get you.

Hopefully there's at least a couple of FAT supercharger owners here... They certainly don't seem to be too common, but from what I can tell it's a really nicely done system.

This is for a Cessna 205. It'd have to be field approval, which when I first heard that I was like "yeah right that'll never happen," but I found out some other people have been successful working with them to get the field approval done and they say they've done some field approved IO-470S's, so maybe there's hope. I do believe there is a wastegate of sorts (popoff?) so you just go full throttle and that will maintain full sea-level rated MP (28" not 29" for what it's worth) through 7,000'. So yes, it's a "turbo-normalizer" not a "turbocharger". After the critical altitude, MP decays as if 7,000' were your sea-level (i.e. MP available at 12,000 feet would be equivalent to 5,000 feet, so roughly about 23-24").

It seems like a great solution for my use case. My main goal is to get better takeoff and climb performance (not cruise speed) and our DAs on bad days are usually not much more than 8,500' (where the stock IO-470 would get 188hp, the IO-550 would get 217hp, and the supercharged IO-470 would get probably about 245hp, for comparison's sake). I don't really want to run a hot turbocharger (been there, done that), and I don't really see myself operating much over 12,500, although the option would be nice. I also don't really want the higher cruise fuel flows of a turbo'ed plane, and I suspect the FAT system will run a lot cooler and with a lot more reasonable fuel flows in cruise than the comparable turbo (this is partly due to lower power being produced, which is okay, but also because you shouldn't have as much cooling issues). The biggest downside is adding 35lbs to the nose of an already nose-heavy plane, and the price tag (but to be honest, the price tag seems reasonable compared to replacing the engine with an IO-550, which requires a new prop as well - we're talking $70k for that engine swap, which is crazy). I'm guessing an IO-550 would also add weight to the nose over the stock engine, but don't know how much or if that's actually true.

 

[flyingcheesehead]

This is for a Cessna 205. It'd have to be field approval, which when I first heard that I was like "yeah right that'll never happen," but I found out some other people have been successful working with them to get the field approval done and they say they've done some field approved IO-470S's, so maybe there's hope. I do believe there is a wastegate of sorts (popoff?) so you just go full throttle and that will maintain full sea-level rated MP (28" not 29" for what it's worth) through 7,000'. So yes, it's a "turbo-normalizer" not a "turbocharger". After the critical altitude, MP decays as if 7,000' were your sea-level (i.e. MP available at 12,000 feet would be equivalent to 5,000 feet, so roughly about 23-24").

It seems like a great solution for my use case. My main goal is to get better takeoff and climb performance (not cruise speed) and our DAs on bad days are usually not much more than 8,500' (where the stock IO-470 would get 188hp, the IO-550 would get 217hp, and the supercharged IO-470 would get probably about 245hp, for comparison's sake). I don't really want to run a hot turbocharger (been there, done that), and I don't really see myself operating much over 12,500, although the option would be nice. I also don't really want the higher cruise fuel flows of a turbo'ed plane, and I suspect the FAT system will run a lot cooler and with a lot more reasonable fuel flows in cruise than the comparable turbo (this is partly due to lower power being produced, which is okay, but also because you shouldn't have as much cooling issues). The biggest downside is adding 35lbs to the nose of an already nose-heavy plane, and the price tag (but to be honest, the price tag seems reasonable compared to replacing the engine with an IO-550, which requires a new prop as well - we're talking $70k for that engine swap, which is crazy). I'm guessing an IO-550 would also add weight to the nose over the stock engine, but don't know how much or if that's actually true.

Very cool. (Literally... ) Sounds like it would be a good solution for your situation. If the 205 is your "forever plane" then you might as well go for it! And I think the supercharger would be easily removed someday if FAT goes away and the system isn't supported any more, though hopefully that's far in the future (and a couple of owners down the road for the plane too).

Google can probably find you the weights of the IO-470 and IO-550 pretty easily... But yeah, those engine swaps are expensive. Even just turning mine up from 280hp to 310hp with a new prop and governor on the same engine is pretty expensive.

I thought the popoff valves on the FAT system were for quick "oopsies" where you had a transient overboost, not for general operation - You might want to double check that. I saw it as a downside of the system, somewhat like the planes that have throttle-linked or fixed wastegates.