[Finley Atherton]

Can anyone give me a formula for how TAS will change as density altitude changes if HP is kept constant?
For example, after careful testing I know that at 8,500 ft DA I have a TAS of about 150 kts at 2,250 rpm and 6 g/h leaned to around peak or just LOP (50% power from Lycomings Part Throttle Fuel Consumption chart).
If I fly at say, 1,000 ft DA at the same power settings (same HP) what would be the predicted TAS.

Fin
9A. 0-320, Hartzell

 

[elippse]

That's a hard one. For a given configuration, such as an RV-6, it will change about 1.1%/1000'. For my plane, it changes about 0.6%/1000'. From 4000' to 10,000' the density changes 20.3% Over that same span, the engine power changes 22.9%, so that the engine power, relative to the density, decreases 0.4% faster. That's one of the reasons planes with normally-aspirated engines fly slower with increasing altitude; their power falls off faster than their parasite drag. Why the difference between the two planes shown above? Induced drag! An RV-6 has a 4.8:1 aspect ratio, while my plane has 8.05:1. The higher you fly and the more weight you carry the more you will slow down due to induced drag, along with the power decrease.

 

[hevansrv7a]

A work-around

I can't give you a formula, but I can suggest a work-around. Pick one of the spreadsheets linked below my signature (third link). Put in your airplane's drag data. Or use the 6A for an example.

Pick a few situations such as 2000', 4000' and so on. You can put in your assumptions about prop efficiency (in real life it is not a constant). Then you can quickly, iteratively solve for equal HP at each DA, changing IAS which then shows TAS. You can chart your results.

Cumbersome, but it will be the most correct answer. Again - be cautious about the prop efficiency which does change and not always the same because different props are optimized differently.

This is a good way to approach the problem because even your V l/d max changes with altitude. Lots of variables, all handled by the spreadsheet.

 

[Kevin Horton]

Can anyone give me a formula for how TAS will change as density altitude changes if HP is kept constant?
For example, after careful testing I know that at 8,500 ft DA I have a TAS of about 150 kts at 2,250 rpm and 6 g/h leaned to around peak or just LOP (50% power from Lycomings Part Throttle Fuel Consumption chart).
If I fly at say, 1,000 ft DA at the same power settings (same HP) what would be the predicted TAS.

We can easily predict changes in TAS vs Density Altitude if we assume the propeller efficiency and drag coefficient do not change. This prop efficiency = constant assumption is probably reasonable for small changes in density altitude and rpm, but it is less and less accurate as we make significant changes in density altitude or rpm. The drag coefficient = constant assumption is true if the angle of attack is constant, but it gradually falls apart as the AOA changes. So, this prediction will not be completely accurate for large changes in CAS or weight.

If prop efficiency, power and AOA are constant, the TAS will vary with the cube root of the air density. If we insert the equation for density altitude, we end up with this ugly guy:

TAS2 = TAS1 *(((1-0.0000068755856*HD1)^4.2556)/((1-0.0000068755856*HD2)^4.2556))^0.33333



where:
TAS1 = TAS determined at density altitude 1
TAS2 = predicted TAS at density altitude 2
HD1 = Density Altitude 1 (units of feet)
HD2 = Density Altitude 2 (units of feet)

If we plug in TAS1 = 150 kt, HD1 = 8500 and HD2 = 1000, we get a predicted TAS of 139 kt.

Please note that with this much change in density altitude, the prop efficiency and AOA will both have changed, so this prediction will not be perfectly accurate. But it should be in the right ballpark.

 

[hevansrv7a]

The question assumed constant BHP

The question assumed constant BHP. Given that constraint, using my own airplane's drag parameters for a starting point, I got this:
Prop=80%

DAlt CASmph TASmph BHP
2000 150.0 154.49 92.08
4000 147.8 156.84 92.02
6000 145.7 159.36 92.14
8000 143.4 161.75 92.07
10000 141.1 164.19 92.07
12000 138.7 166.59 92.02

This was all done quickly and iteratively using the model spreadsheet that can be found on the links below. No user-math required. All the previous caveats about prop efficiency and even engine efficiency still apply. This is hypothetical to that extent.

 

[DGlaeser]

Rule of thumb

You get pretty close by adding 2% per thousand feet of altitiude to your IAS. So at 5K you add 10%.
A lot easier to figure in your head than Kevin's formula And you don't need Howard's spreadsheet loaded on your PDA

 

[hevansrv7a]

Not the same question?

You get pretty close by adding 2% per thousand feet of altitiude to your IAS. So at 5K you add 10%.
A lot easier to figure in your head than Kevin's formula And you don't need Howard's spreadsheet loaded on your PDA

Either this answers a different question or it conflicts pretty directly with my spreadsheet. In mine, for increasing altitude and equal BHP, the IAS (CAS) went down even though the TAS went up. In Dennis's rule, the IAS goes up. It can't all be right.

 

[RVbySDI]

I can't give you a formula, but I can suggest a work-around. Pick one of the spreadsheets linked below my signature (third link). Put in your airplane's drag data. Or use the 6A for an example.

Pick a few situations such as 2000', 4000' and so on. You can put in your assumptions about prop efficiency (in real life it is not a constant). Then you can quickly, iteratively solve for equal HP at each DA, changing IAS which then shows TAS. You can chart your results.

Cumbersome, but it will be the most correct answer. Again - be cautious about the prop efficiency which does change and not always the same because different props are optimized differently.

This is a good way to approach the problem because even your V l/d max changes with altitude. Lots of variables, all handled by the spreadsheet.

I am looking at your "Glide Ratio & Angle with Cruise power" spreadsheet. Is this the spreadsheet you are recommending we use? On that spreadsheet, can you tell me what the "Ratio Ground/Vertical" field is representing? Also, am I assuming the "Glide Airspeed" is IAS? If so, how do I use this spreadsheet to determine TAS?

 

[hevansrv7a]

What I meant to say..

I am looking at your "Glide Ratio & Angle with Cruise power" spreadsheet. Is this the spreadsheet you are recommending we use? On that spreadsheet, can you tell me what the "Ratio Ground/Vertical" field is representing? Also, am I assuming the "Glide Airspeed" is IAS? If so, how do I use this spreadsheet to determine TAS?

Oops, I'm sorry!

There are two boxes on that page. The box on the left ("Workbooks") contains various versions of the same spreadsheet. Each version is for a different airplane. The airplanes were picked, mostly, because we have very solid data about their drag curves. The outlier is my own airplane. You can download and modify any of those spreadsheets. That is what I was recommending for this thread. Unfortunately, I don't have the RV-9 in there because CAFE did not use the Zero Thrust device on a "9". The spreadsheet and the presentation explain how to get one's own numbers to plug in.

The box on the right ("Documents and Aids") is misc. stuff, including the last one, a spreadsheet on "Glide Airspeed..". That one is pretty simplistic but solves other problems. Those speeds are necessarily TAS because you are dealing with what the airplane is doing, not what it says it is doing. Thus, ground/vertical is the actual ratio of the horizontal distance versus the vertical distance in a given time such as a minute. That's a true glide ratio, not necessarily L/D but certainly closely related to it. This one gives useful insights, but does not help you determine TAS, just uses it.

I'm thrilled that somebody looked. PM me or email me with a phone# if you want to get some personal help with anything on that page.

 

[Finley Atherton]

Thanks for the considered replies to my Post #1. It seems to be more complicated than I imagined. I was sort of hoping there may be a simple, approximate rule of thumb formula.
For flight planning purposes, I wanted to construct a table of true airspeeds at varying altitudes at three of my favored power settings. I realized I did not know this information recently when I was forced to cruise at low altitude due to weather.
I think I will go and do some flights to determine the actual true airspeeds and it will be interesting to see if they correlate to the answers calculated by the suggested methods.
Unfortunately I don't have anything that displays TAS directly so it will take some time using the NTPS method to determine TAS - sounds like a good excuse to do lots of flying.

Fin
9A

 

[Bob Redman]

TAS RULES OF THUMB

G'day Finley,

Rough Rules of thumb used by BFTS Tamworth to estimate TAS for low nav training on the CT-4B are as follows:

a. add 2kt to KIAS for each 1000ft above MSL.
b. add 2kt to KIAS for each 5degC above ISA.

Hope this helps.

Regards,

Bob Redman

 

[elippse]

I got away from the "same horsepower" thingy in the original post. So if you maintained the same power with an increase of altitude, the parasite drag would decrease but the induced drag would increase but not as much, causing the plane to go faster. How much would depend upon the plane's aspect ratio. With a lower aspect ratio wing, the plane flies with a much higher nose attitude which may also increase the parasite drag slightly.
With a normally aspirated engine, to keep the power the same, you would have to start off with less power down low, and increase it as you go up. With a supercharged engine it would be no problem up to the supercharger's critical altitude.
In both of these cases it is somewhat difficult to know what the real power is, since you have to know both MAP and induction temperature to determine the charge density. There is also the little thing of reduced exhaust back pressure allowing the cylinders to fill more.
With a supercharged engine you must take into account that the temperature out of the compressor depends on the input-output pressure ratio, so as you go higher, the pressure ratio for a given MAP increases, and the induction temperature gets even hotter. That, along with MAP, must be accounted for.

 

[Finley Atherton]

G'day Finley,

Rough Rules of thumb used by BFTS Tamworth to estimate TAS for low nav training on the CT-4B are as follows:

a. add 2kt to KIAS for each 1000ft above MSL.
b. add 2kt to KIAS for each 5degC above ISA.

Thanks Bob. I am thinking about what you have said but I don't think it answers my original question in Post #1 involving keeping the power constant.
I am near Armidale. Contact me if you plan to be up this way sometime and you want to talk Rvs.

In both of these cases it is somewhat difficult to know what the real power is, since you have to know both MAP and induction temperature to determine the charge density. There is also the little thing of reduced exhaust back pressure allowing the cylinders to fill more.
With a supercharged engine you must take into account that the temperature out of the compressor depends on the input-output pressure ratio, so as you go higher, the pressure ratio for a given MAP increases, and the induction temperature gets even hotter. That, along with MAP, must be accounted for.

I stand to be corrected but I have calculated power using rpm and FF at "Best Economy" mixture settings without any reference to MAP, induction temperature or altitude. Specifically, page 3-12 of the I0-320 Operators Manual which can be seen on Aerosports web site here
Using this chart and the settings from Post #1 the engine is putting about 80 hp. If I change altitude but once there replicate the rpm and FF with the mixture again leaned to "Best Economy" (which Lycoming defines as peak EGT), I presume the engine would again be producing about 80 hp?

Fin

 

[elippse]

There's only one method that I know of to obtain the true horspower of an engine in flight and that's with a calibrated torque sensor on the propshaft and an accurate tach. Sure, you can estimate horsepower from FF if you know the SFC, and I'm sure you can get within a few percent. But how do you know what the SFC is, and whether your FF is calibrated? Those are just estimates, too.

 

[Finley Atherton]

There's only one method that I know of to obtain the true horspower of an engine in flight and that's with a calibrated torque sensor on the propshaft and an accurate tach. Sure, you can estimate horsepower from FF if you know the SFC, and I'm sure you can get within a few percent. But how do you know what the SFC is, and whether your FF is calibrated? Those are just estimates, too.

I agree with what you are saying and the HP calculation is further muddied by our non standard RV installations which may have electronic ignition, higher compression and straight through exhaust pipes, but if I can easily calculate HP within a few % then this should be good enough for my purposes. Also referring back to Post #1, I am not so much interested in actual HP rather I want to fly at the same HP at varying heights and setting the same rpm and FF at the same mixture setting (Best Economy) should achieve this.

As far as working out the actual HP I don't need to know the SFC because Lycoming has worked it out at both "Best Power" and "Best Economy" for a range of FF and RPMs and incorporated it into the graph I referenced in Post # 13. Presumably Lycoming thinks calculating HP from FF and rpm at two particular mixture settings is reasonably accurate or they would not have the graph in their Operating Manual.

I agree with what you say about the accuracy of FF readings. I have made the extra effort of draining a tank, filling with a known quantity, flying at my normal cruise FF (6 g/h) for a set time on that tank, draining and calculating the real FF and then calibrating the FF gauge.

Fin
9A

Fin
9A