Horsepower required for same airspeed at higher altitude

[dtuuri]

If I wanted to do the computations in real-time while I was in my airplane, climbing, at each thousand-foot increment, how would I do it?

You'd have to level off at each altitude, note the IAS at the proper power setting and add 2% for each 1000'. Let Wolfgang tell you how:

"There is a rule of thumb that, in order to get your true air speed, you must add 2 per cent to your indicator reading for every thousand feet of altitude. For example, if your indicator reads 100 m.p.h. and your altitude is 5,000 feet, your true air speed is 100, plus five times 2 per cent of 100; that adds up to 110 m.p.h. "​

 

[David Megginson]

Nope. Keep on reading, lots of more good gems. Like this for example:

"Next in the logics of high altitude, there is an engineering fact that is sometimes overlooked when pilots discuss an airplane's altitude behavior: At higher altitude, the airplane needs more power. In any given flight condition— such as flat cruising flight or slightly mushing flight or nearly stalled flight—it will fly faster at the higher altitude; it will fly faster without additional drag. But it nevertheless will need more power."​

I would suggest a different source for aerodynamics. Langwiesche is the best for basic flying technique even almost 80 years later, but he's deliberately a bit fuzzy on the theory (he makes it clear in his intro that the book won't be about that).

The EAS stays constant. The CAS and IAS will start to underread noticeably above 10,000 ft and/or 200 kt because of compressibility errors — that's why higher-performance aircraft have lower Vne (in IAS) specified for higher altitudes.

But for the most part (with variations for specific aircraft) the answer to the OP's question is yes, IAS will typically remain close to constant for the same power setting under the same flight conditions from sea level to 10,000 ft. If in doubt, check your POH for any model-specific quirks (mine has CAS constant within ½ kt).

Caveats:

1. Holding a constant altitude in a subsiding airmass (eg under a higher pressure system) your IAS will be a few knots slower; in rising air (e.g. thermals, cumulus cloud, ridge lift) it will be a few knots faster.
2. Higher gross weight slows you down at the same power setting (the rule of thumb — very approximate — is 1 knot per 100 lb for a PA-28 or C172).
3. A forward CG costs you a knot or two (but makes your pitch more stable in turbulence); an aft CG buys you a knot or two (but makes your pitch less stable in turbulence).

The caveats are why we use RPM rather than IAS to set power with a fixed-pitch prop.

 

[Checkout_my_Six]

If I wanted to do the computations in real-time while I was in my airplane, climbing, at each thousand-foot increment, how would I do it?

I’d match the “true airspeed” with a power setting and fuel flow. Those settings at altitude & oat will tell you the difference in HP.

 

[dtuuri]

I would suggest a different source for aerodynamics.

LOL! That's what I was thinking about your post citing Stick and Rudder as pertained to not making small rudder turns when following a localizer—that YOU should find a different source, since Mr. Langewiesche probably didn't know much about those in the early '40s.

But here he's spot on and you're just not going to admit you're wrong no matter what. All the POHs cited above verify that for a given power CAS will go down (compressibility is negligible at these speeds). So, argue away if you must, but that's it for me. Bye.

 

[birdus]

https://www.investopedia.com/ask/an...-compounding-interest-and-simple-interest.asp

I assume the article says something about Euler's number. Moreover, I assume you don't really know the answer to the question. Doesn't really matter. It's not that important.

 

[asicer]

I assume the article says something about Euler's number. Moreover, I assume you don't really know the answer to the question. Doesn't really matter. It's not that important.

The answer is similar to that in post #81.

Here's the Lycoming chart for the 200hp IO-360:

 

[David Megginson]

Nope. Keep on reading, lots of more good gems. Like this for example:

"Next in the logics of high altitude, there is an engineering fact that is sometimes overlooked when pilots discuss an airplane's altitude behavior: At higher altitude, the airplane needs more power. In any given flight condition— such as flat cruising flight or slightly mushing flight or nearly stalled flight—it will fly faster at the higher altitude; it will fly faster without additional drag. But it nevertheless will need more power."​

By "more power" at higher altitude, Langwiesche almost certainly meant "higher RPM" and/or "further-open throttle", both of which are correct (but not the way modern POHs use "power").

I'm attaching the performance table from my Piper PA-28-161 POH. If you pull out your E6B, you'll see that at 75% power, the CAS is the same at sea level and 8,000 ft DA, but that at 65% and 55%, it falls off a bit (also apparent from the different slope of the lines). That shows how quirky it can get even for the same plane. In my case, the dropoff at 65% power and 55% power is probably because I have a fixed-pitch propeller that's optimised for just one CAS, so it loses a bit of efficiency in the lower power settings.

 

[asicer]

I'm attaching the performance table from my Piper PA-28-161 POH. If you pull out your E6B, you'll see that at 75% power, the CAS is the same at sea level and 8,000 ft DA

The chart's kind of fuzzy (low res). Are you getting 124KTAS at 8000DALT and 113KTAS at 0DALT?

 

[dtuuri]

The chart's kind of fuzzy (low res). Are you getting 124KTAS at 8000DALT and 113KTAS at 0DALT?

I agree with this. I got 126 KTAS/113KTAS. I also get 9000' DA which comes out via E6b to 109-110 CAS to make the 126.

 

[David Megginson]

The chart's kind of fuzzy (low res). Are you getting 124KTAS at 8000DALT and 113KTAS at 0DALT?

127 KTAS at 8,000 DA. It is fuzzy (I took it from the PDF version, which Piper didn't put a lot of effort into; the paper is easier to read).

Funny coincidence: 124 KTAS happens to be the best I can manage at 75% power in real life, under ideal conditions (which are rare in flying).

 

[sarangan]

I would suggest a different source for aerodynamics. Langwiesche is the best for basic flying technique even almost 80 years later, but he's deliberately a bit fuzzy on the theory (he makes it clear in his intro that the book won't be about that).

The EAS stays constant. The CAS and IAS will start to underread noticeably above 10,000 ft and/or 200 kt because of compressibility errors — that's why higher-performance aircraft have lower Vne (in IAS) specified for higher altitudes.

But for the most part (with variations for specific aircraft) the answer to the OP's question is yes, IAS will typically remain close to constant for the same power setting under the same flight conditions from sea level to 10,000 ft. If in doubt, check your POH for any model-specific quirks (mine has CAS constant within ½ kt).

Caveats:

1. Holding a constant altitude in a subsiding airmass (eg under a higher pressure system) your IAS will be a few knots slower; in rising air (e.g. thermals, cumulus cloud, ridge lift) it will be a few knots faster.
2. Higher gross weight slows you down at the same power setting (the rule of thumb — very approximate — is 1 knot per 100 lb for a PA-28 or C172).
3. A forward CG costs you a knot or two (but makes your pitch more stable in turbulence); an aft CG buys you a knot or two (but makes your pitch less stable in turbulence).

The caveats are why we use RPM rather than IAS to set power with a fixed-pitch prop.

Langwiesche's book might be okay for a nontechnical person trying to understand flight, but I find it is unnecessarily long winded.

So basically, you're describing the difference between CAS and EAS (?)

Yes, it is EAS, but the difference between IAS, EAS and CAS is minimal at cruise speed anyway.

I think calling IAS "speed" has lead to all sorts of misinterpretations. It would have been better if it were shown in psi as differential dynamic pressure.

The propulsion power is actually proportional to the product of IAS and TAS. At first that seems very odd to be multiplying two speeds, but if you think of IAS as pressure, then it makes a lot more sense.

 

[David Megginson]

Langwiesche's book might be okay for a nontechnical person trying to understand flight, but I find it is unnecessarily long winded.

That's fair, but in his defence, it's long-winded because it was written for a time when civilian pilots had relatively little knowledge about how their planes actually flew. As he mentioned in his introduction, there were highly-technical aerodynamic treatises that were inaccessible to a pilot without an engineering degree, or folksy books of flying advice that was mostly wrong (and often dangerous), but nothing in-between. For civilian pilots, there were no POHs with anything like power-setting tables, little information about what happened inside their engines, and even the E6B was barely in civilian use. It always takes more words to explain something when you can't use specialised jargon, and Langwiesche did a pretty-good job — sometimes it's confusing because he uses different terminology than we use today ("flippers" instead of "elevators", and "power" for the throttle setting rather than % power), but it mostly still stands up after 77 years.

It would have been better if it were shown in psi as differential dynamic pressure.

Quite true, and it would also make more sense if the altimeter simply showed ambient air pressure without trying to calibrate it in feet, but then neither would be much practical use to pilots in the air.

The propulsion power is actually proportional to the product of IAS and TAS. At first that seems very odd to be multiplying two speeds, but if you think of IAS as pressure, then it makes a lot more sense.

My understanding (not an engineer, so please correct if needed) is that as you get into "thinner" air, you have less drag to slow you down, but also have to fly faster to get the same dynamic pressure (q) for lift, so the two more-or-less balance out to the same power result for Power = Thrust * Velocity.

There are gotchas, of course — a CS propeller is less efficient when it's spinning faster due to friction losses and, in the extreme case, the tips going supersonic (which we try to avoid); a fixed-pitch prop is optimised for only one CAS/EAS, and will lose performance at any other (as is the case in my Piper PA-28-161); our normally-aspirated engines have max ceilings for any given power setting; etc. etc.

 

[sarangan]

Quite true, and it would also make more sense if the altimeter simply showed ambient air pressure without trying to calibrate it in feet, but then neither would be much practical use to pilots in the air.

Good point, but there is a difference. Altimeter is also used for obstacle avoidance, so the being able to compare your altimeter to numbers published on charts is important at low altitudes. Above 18k, that's not relevant, so we use pressure altitude. So, at 35k, you could actually be a couple of thousands of feet off, but it doesn't matter as long as all pilots use the same instrument for vertical seperation. Pressure would be more meaningful than feet (human performance, cabin differential pressure are typically expressed in psi rather than feet). But having two different units for the same instrument would overly complicate things.

For airspeed, does it really matter if the final approach speed is 0.5 psi instead of 60 knots? That 60 really doesn't mean you are travelling at 60 nautical miles per hour over ground. It could be 60 ham sandwiches, and as long as we agree on a number that's really all that matters. What cracks me up are the metric advocates who push their agenda into aviation, as if dividing by 10 is a critical exercise in flying. Its not like feet of altitude, knots and mph of speed are really what they imply.

My understanding (not an engineer, so please correct if needed) is that as you get into "thinner" air, you have less drag to slow you down, but also have to fly faster to get the same dynamic pressure (q) for lift, so the two more-or-less balance out to the same power result for Power = Thrust * Velocity.

That's correct. But the confusion often lies in velocity. It is true airspeed, not indicated air speed or ground speed. If you maintain the same power at a higher altitude, your thrust will be lower and velocity will be higher. That seems obvious now, but it wasn't so obvious when I first started looking at it.

There are gotchas, of course — a CS propeller is less efficient when it's spinning faster due to friction losses and, in the extreme case, the tips going supersonic (which we try to avoid); a fixed-pitch prop is optimised for only one CAS/EAS, and will lose performance at any other (as is the case in my Piper PA-28-161); our normally-aspirated engines have max ceilings for any given power setting; etc. etc.

Actually, a CS propeller becomes less efficient at both ends. At high RPM and low pitch setting, the high crankshaft rotation will result in more friction losses. Going supersonic would make it significantly worse. At the other end, a high pitch angle will produce more induced drag resulting in a lower efficiency.

 

[Tantalum]

I'm all for changing published V speeds into ham-sandwich units

 

[EdFred]

I'm all for changing published V speeds into ham-sandwich units

And while we are at it, I want horsepower changed to llamathrust.

 

[MauleSkinner]

And while we are at it, I want horsepower changed to llamathrust.

But how do llamas create thrust? That might not be good for aviation.

 

[EdFred]

But how do llamas create thrust? That might not be good for aviation.

Dunno, just saw this somewhere:

 

[David Megginson]

For airspeed, does it really matter if the final approach speed is 0.5 psi instead of 60 knots? That 60 really doesn't mean you are travelling at 60 nautical miles per hour over ground. It could be 60 ham sandwiches, and as long as we agree on a number that's really all that matters. What cracks me up are the metric advocates who push their agenda into aviation, as if dividing by 10 is a critical exercise in flying. Its not like feet of altitude, knots and mph of speed are really what they imply.

I enjoy friendly discussions like this -- if it doesn't feel like that, please feel free to drop out with no hard feelings.

I think airspeed (vs just dynamic pressure) does matter still somewhat, and used to matter a lot. Before GPS, and even more so before DME (if if you weren't flying directly to/from the DME station), you needed your airspeed calibrated in knots (or km/h) just as much as you needed your altimeter calibrated in feet (or metres). Certainly you could have converted, but you could have converted the altimeter from inHg or mbar to feet as well.

I do grant your point that starting with IAS is a bit more complicated. With the altimeter, you need to put the right setting in the Kollsman window and (if the weather's cold and terrain clearance is an issue) convert from indicated to true altitude, and that's about it. Even with the ASI calibrated for nominal airspeed, for navigation purposes you need to convert from IAS to CAS, and then from CAS to EAS (at high speed or altitude), then from EAS to TAS, then (based on what you know about the winds) from TAS to GS, which was a fair bit of work (hence the separate navigator's position in golden-age airliners).

Actually, a CS propeller becomes less efficient at both ends. At high RPM and low pitch setting, the high crankshaft rotation will result in more friction losses. Going supersonic would make it significantly worse. At the other end, a high pitch angle will produce more induced drag resulting in a lower efficiency.

Good point. The general rule of thumb I see is to use the lowest RPM and the highest MP allowed by your POH tables for any given power setting; I'll assume that avoids the low-RPM inefficiencies.

Cheers, David

 

[sarangan]

I enjoy friendly discussions like this -- if it doesn't feel like that, please feel free to drop out with no hard feelings.

With that, you have proven that you are a true Canadian . I am also from Canada, actually got my private pilot certificate in Ottawa, but I moved south a long time ago. Back to your point, one thing we do poorly in the U.S is maintaining a civil discourse while disagreeing. Makes me feel nostalgic.

 

[Salty]

I'm all for changing published V speeds into ham-sandwich units

Buddy of mine uses "potatoes" when we're in his Nanchang because a lot of the instruments are in meters and kph, etc, it's less confusing to just say potatoes.

 

[David Megginson]

With that, you have proven that you are a true Canadian . I am also from Canada, actually got my private pilot certificate in Ottawa, but I moved south a long time ago. Back to your point, one thing we do poorly in the U.S is maintaining a civil discourse while disagreeing. Makes me feel nostalgic.

Wonderful. Where did you train in Ottawa? I got my PPL and IR at the Ottawa Flying Club in 2002–03 (I'm based at Rockcliffe now).

Speaking of moving south, my younger daughter moved to North Carolina on Sunday to start her Ph.D. at UNC Chapel Hill. She's finding the culture a bit different so far, but is impressed at how genuinely friendly the people are.

 

[David Megginson]

Buddy of mine uses "potatoes" when we're in his Nanchang because a lot of the instruments are in meters and kph, etc, it's less confusing to just say potatoes.

There's some other vegetable some pilots swear by instead of V-speeds -- I think it's called the eh-oh-eh (or something like that).

 

[Tantalum]

Buddy of mine uses "potatoes" when we're in his Nanchang because a lot of the instruments are in meters and kph, etc, it's less confusing to just say potatoes.

The beauty of EA is that nothing would stop you from doing this!

 

[Tusayan]

Bloviating without end and expecting others to listen or step out of the way without objection does indeed seem to be a Canadian characteristic, at least I’ve noticed it… but then again few people take Canadians seriously so it makes no difference

Units make very little difference except if you are unfamiliar with how many ‘potatoes’ is too many or too little.

 

[sarangan]

Wonderful. Where did you train in Ottawa? I got my PPL and IR at the Ottawa Flying Club in 2002–03 (I'm based at Rockcliffe now).

Speaking of moving south, my younger daughter moved to North Carolina on Sunday to start her Ph.D. at UNC Chapel Hill. She's finding the culture a bit different so far, but is impressed at how genuinely friendly the people are.

Ottawa Aviation Services based at CYOW. Back in 1996 it was a reputable school run by an Air Canada pilot and his family. Last I heard, it was run into the ground by new owners.

 

[David Megginson]

Ottawa Aviation Services based at CYOW. Back in 1996 it was a reputable school run by an Air Canada pilot and his family. Last I heard, it was run into the ground by new owners.

Yes, that's correct — OAS went out of business and some of the students lost a lot of money.