M

MTBehnke

Well Known Member
This morning I did some 4-way GPS test runs to verify TAS at various RPM settings. The data I collected fits nicely with the curve fit I had Excel calculate:

RPMvsKTAS.JPG


I did all the testing at a density altitude of 6000 feet.

My question is whether there's a simple equation I can use to offset this curve for different density altitudes (e.g. 4000, 8000 ft) vs. burning a bunch more fuel to repeat the test at different altitudes.

My RV-9A has a fixed pitch Catto 3-blade.

Thanks,
 
I am surprised that it is so close to linear. Unless you have a pressing need for hard data, I would just pick an RPM that you will use most of the time, use that TAS or close to it for flight planning purposes and just accept whatever you get once you get airborne.

In six years of flying my 6A, the only time I really calculated arrival times to the minute was overflying Cuba.
 
I guess I'm not necessarily looking for a high degree of accuracy - the geek in me is just trying to better understand how things work.

I looked at an old C172 manual which shows TAS decreasing slightly with increasing density altitude - about a knot per 2000 feet - for a given RPM. This is the opposite effect of what I was assuming would happen.

Either way - density altitude doesn't appear to have a real significant effect on TAS at a constant RPM so my 6000' DA chart is probably pretty good for estimating.
 
From my Flight Computer

I have a flight data recorder that came with software to do plotting and regression analysis. I have been doing a few test again this week (just because I like data). I plot a bit different then you did but you can figure out your question from this graph. It looks like the slope of the curve is an increase in TAS of 2.2 kts for every 1000 ft increase in density altitude. These numbers are for leaning to peak EGT. I am working the curves for full rich and max power (150 deg rich of peak EGT). May post later if I get the data.

cruiseperform.jpg
 
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I've seen data from Larry Pardue, IIRC, that showed that on his RV-6 with Sensenich FP prop, TAS vs RPM was pretty much the same at all altitudes up to the mid-teens. If you think about it, the prop is sort of like a screw - if the aircraft had zero drag, and there was zero "slippage", you'd get a particular TAS for a given rpm, no matter what the altitude. In real life, with an aircraft that has some drag, there is probably a small variation in TAS vs rpm as you change altitude, but this variation may be quite small.
 
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MTBehnke said:
snip
My question is whether there's a simple equation I can use to offset this curve for different density altitudes (e.g. 4000, 8000 ft) vs. burning a bunch more fuel to repeat the test at different altitudes.
snip
Click to expand...

Mike, repeating the tests are called "excuses to fly".
 
Fast 6A

plehrke said:
I have a flight data recorder that came with software to do plotting and regression analysis. I have been doing a few test again this week (just because I like data). I plot a bit different then you did but you can figure out your question from this graph. It looks like the slope of the curve is an increase in TAS of 2.2 kts for every 1000 ft increase in density altitude. These numbers are for leaning to peak EGT. I am working the curves for full rich and max power (150 deg rich of peak EGT). May post later if I get the data.

cruiseperform.jpg
Click to expand...

Wow, you have a fast 6A! Is that TAS calibrated?

Hans
 
nucleus said:
Wow, you have a fast 6A! Is that TAS calibrated?

Hans
Click to expand...

No. Those TAS are off of IAS. I am also in process of redoing my calibration curves. One of the issues I have found is that the data recorder is about 5 degs high in OAT. That will push the curves about 300 ft down in density altitude and a couple kts left in TAS calculations. The curves should have the same slope which was the answer to the original question by MTBehnke on how to offset his curve for different density altitudes.
 
RPM vs. TAS

Now that I have my plane painted I decided to re-try a 4-way gps speed run and see if there was any change in TAS. With the FP Catto 3-blade I was able to chart out a graph of RPM vs. TAS as you can see in the first post in this thread.

Before, with bare skins and primer on the fiberglass surfaces I'd see 157 kts at 2600 rpm. I also had prop guard tape on the blades, which supposedly causes about a 1-2 kt loss.

Later I sanded the primer surfaces much smoother and think I picked up about 1-2 kts.

Now that I'm fully painted (and for now without the leading edge prop tape) I was running 166 kts at the same 2600 RPM - a 9 knot increase over my original numbers. If I project it out I should be right on or maybe slightly above the speeds Craig Catto quoted me.

Sweet!
 
Effective pitch

Using the screw analogy, basically a FP prop on a given airplane will have an effective pitch, in un-accelerated flight, which is the distance, in inches, that the plane and prop travel forward in one revolution of the prop. A similar plane with higher drag and the same prop will show lower effective pitch, and a similar plane with less drag and the same prop will show higher effective pitch. That's because the AOA will be different due to loading, just as a wing AOA will vary with weight at a given speed. That is also why geometric pitch is unreliable. To obtain the effective pitch, multiply TAS mph X 1056 / rpm. For this to be correct, the TAS will have to be from a calibrated pitot-static system. The more efficient your prop, the more this number will remain constant over a range of, say, 2200-2800 rpm. The highest value is where it is most efficient, and when it drops off that shows you where you have reached peak efficiency and now the effciency is dropping off. Less-efficient props will show a narrower range, while the higher the prop's efficiency, the wider this range will be. That is because the twist distribution is correct and the thrust torque-ratio of every inch of radius is almost constant. If the thrust-torque ratio isn't constant along the span it's because the twist and the thrust span-wise distribution from chord distribution is less than optimum. Prandtl had it right!
 
Nomenclature quibble

elippse said:
Using the screw analogy, basically a FP prop on a given airplane will have an effective pitch, in un-accelerated flight, which is the distance, in inches, that the plane and prop travel forward in one revolution of the prop. A similar plane with higher drag and the same prop will show lower effective pitch, and a similar plane with less drag and the same prop will show higher effective pitch. That's because the AOA will be different due to loading, just as a wing AOA will vary with weight at a given speed. That is also why geometric pitch is unreliable. To obtain the effective pitch, multiply TAS mph X 1056 / rpm. For this to be correct, the TAS will have to be from a calibrated pitot-static system. The more efficient your prop, the more this number will remain constant over a range of, say, 2200-2800 rpm. The highest value is where it is most efficient, and when it drops off that shows you where you have reached peak efficiency and now the effciency is dropping off. Less-efficient props will show a narrower range, while the higher the prop's efficiency, the wider this range will be. That is because the twist distribution is correct and the thrust torque-ratio of every inch of radius is almost constant. If the thrust-torque ratio isn't constant along the span it's because the twist and the thrust span-wise distribution from chord distribution is less than optimum. Prandtl had it right!
Click to expand...
I did some "research" with the Cessna 152. I had as resources the POH and the published work by Jack Norris and Andy Bauer with the "propless" 152. That plus some simple math allows direct evaluation of "effective pitch" and also of "propulsive efficiency". The latter is net of the interactions between the prop stream and the fuse, not the pure prop's performance. This is a long way of saying that propeller efficiency is not the same as effective pitch. I thought it would be, but it's not. The relationship between power in and thrust out is just not the same as the effectiveness of the prop in screwing forward through the air.

This may not be a good analogy, but remember that there is a 14% greater power requirement at best L/D than at minimum sink speeds. Your least power speed is not the most efficient speed.

The link to a page of related information is below my signature. The link to the spreadsheet that demonstrates this is:
http://home.cogeco.ca/~n17hh/Models/C152PropEfficiency.xls
If I have made an error, I'd welcome help in correcting it.
GraphPropEffVsEffPitch.jpg
 
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Effective pitch

Let's look at the results from the post which started this thread. Calculating the effective pitch by TAS mph X 1056 / rpm gives:
rpm kt EP"
1800 101 68.2
1900 109 69.7
2000 117 71.1
2100 124 71.8
2200 131 72.4
2300 138 72.9
2400 144 72.9
2500 151 73.4
2600 157 73.4
2700 162 72.9
As can readily be seen, the effective pitch increases until it peaks at 73.4" at 151-157 kt, then begins to decline. It should be obvious that at the 1800 rpm value it takes more 7.6% more rpm to get the speed, whereas at the peak EP, the maximum speed vs rpm is obtained. Since rpm equates to horsepower, it requires more power to produce the speed at the lower rpm values, showing that the efficiency is less. This is generally the result of the twist and span-wise thrust distribution being less than optimum.
 
Not quite exact (HP and RPM)

elippse said:
Let's look at the results from the post which started this thread. Calculating the effective pitch by TAS mph X 1056 / rpm gives:
rpm kt EP"
1800 101 68.2
1900 109 69.7
2000 117 71.1
2100 124 71.8
2200 131 72.4
2300 138 72.9
2400 144 72.9
2500 151 73.4
2600 157 73.4
2700 162 72.9
As can readily be seen, the effective pitch increases until it peaks at 73.4" at 151-157 kt, then begins to decline. It should be obvious that at the 1800 rpm value it takes more 7.6% more rpm to get the speed, whereas at the peak EP, the maximum speed vs rpm is obtained. Since rpm equates to horsepower, it requires more power to produce the speed at the lower rpm values, showing that the efficiency is less. This is generally the result of the twist and span-wise thrust distribution being less than optimum.
Click to expand...

HP is a function of RPM, MP and altitude. Assuming the data here is from a single altitude, it still does not address HP without MP. The Cessna data does. I'm not pushing any theory here. I'm simply running the numbers for the C-152 that are the best data available and perhaps better than any we have for most RV's.

You could use the Cessna data from the POH (or from my copy of it) to see just how closely the curves fit between RPM and HP. In my doodling with that there was a poor fit.
 
hevansrv7a said:

HP is a function of RPM, MP and altitude. Assuming the data here is from a single altitude, it still does not address HP without MP. The Cessna data does. I'm not pushing any theory here. I'm simply running the numbers for the C-152 that are the best data available and perhaps better than any we have for most RV's.

You could use the Cessna data from the POH (or from my copy of it) to see just how closely the curves fit between RPM and HP. In my doodling with that there was a poor fit.
Click to expand...

My mind tends to go simple with this matter.

HP is a function of fuel burn (assuming proper leaning) and TAS is function of HP. With that premise in place, I have created a personal chart depicting fuel burn and TAS for this airplane and it works. I generally get to where I am going as planned.

MP and RPM are not relevant except for determining when it is safe to lean or determining best power for a max performance climb. MP is the key indicator for leaning starting at 23" or less. The only time I really pay attention to RPM is on take off to confirm the engine is normal and sometimes when doing a max performance climb, I will let it wind up to 2500 and climb at that RPM.

For cruise, TAS is better up high at a given fuel burn due to less drag.

The concept is a KISS theory. It works for me.
 
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