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Old 01-16-2012, 01:00 PM
RV8R999 RV8R999 is offline
Join Date: Dec 2008
Location: na
Posts: 1,458
Default Quantifiying Level Flight Performance

I'm swapping props from a wood sensenich to a composite 3-blade Catto. The sensenich was pitched between cruise and climb but ended up more of a climb prop. I asked Craig to pitch the new prop more toward the cruise.

Sitting here at my desk (between flights) I realised during phase-I I only condcuted a test day conditions level flight performance sweep and didn't really normalize the data - I did it the easy way - record airspeed vs engine power and plot it. This is great for a quick look but doesn't provide an accurate enough baseline for comparisons with future data after any modifications are made, such as a prop change.

Another limitation with the quick look method is it doesn't account for change in aircraft weight from start to finish making the data unusable to extrapolate to conditions other than test day conditions. To fully capture the performance data throughout an airplanes entire envelop would be extremely time consuming and very expensive (fuel). Imagine running the level flight sweep in 500 ft increments from SL to 12,000 at in 5 deg OAT increments from 0-100 deg F! In civil and military flight test this is a NON-STARTER!

So how can we capture the needed data in as few test flights as possible, use it as a baseline to compare after modifications and also extrapolate the to areas of the envelop we have not explored?

There are two basic methods:

The Weight/delta and Weight/sigma method where Delta is the ratio of Ambient pressure at a specific altitude (Pa) and Standard Sea Level Pressure (Pssl) or Delta = Pa/Pssl.

Sigma is the ratio of Density at Altitude (rho) / Standard Sea Level Density (rho ssl).

Both methods utilize the same basic idea - As weight of the aircraft decreases due to fuel burn we need to climb in altitude to maintain the same aerodynamic forces - that is all there is to it. Climb as fuel is burned off.

Heres how it works:

Mathmatically the drag equation contains three independent variables (Speed, Weight, Ambient Pressure). If we pick a value for the ratio of Weight to Pressures we simplify our problem to two variables (W/delta, Speed). If we hold W/delta constant we can now vary our airspeed and record the power required at that W/delta.

For W/delta to remain constant while weight is decreasing due to fuel burn the delta term must decrease as well. Since delta is a ratio of Pa/Pssl and Pssl is constant this means we need to find a lower Pa (ambient pressure). Pressure decreases with altitude. Voila!

You can pick any arbitrary number you want for W/delta but some will be impossible to fly. You can pick a W/delta equal to the max gross weight of the airplane but if you do and ambient temperatures end up as standard day you'll have to fly the first point at zero altitude - Uh oh

My RV8 Max GW is 1800. If I chose a W/delta of 2000 and my actual gross weight on test day is 1600 then I need a delta = 1600lbf/2000 or 0.8.

Remembering Pressure is also a function of Temperature I can look up in atmospheric tables what Pressure altitude for the given temperature gives me a delta of .8. In this case assuming 70 deg F I need to fly the first data point at 6158 ft PA to maintain a W/delta of 2000. As I stabilize and get this first data point I've burned off some fuel - say 0.2 gal. Now my new actual weight is 1598.6 lbf (1600 - (6.02 lbf/gal * .2 gal)). To fly the next data point holding W/Delta constant I need to climb, since my weight decreased by 1.4lbs to a delta of 1598.6/2000 = .7993. We can assume this altitude change will be small so we use the same temp of 70 which results in a new altitude of 6178 ft (20 ft higher) and so on.

The trick is to pick a fuel burn far enough into the future to allow you to fly to the altitude and stabilize on airspeed as the fuel burns to your predicted value. There is some iteration with temperature as well but once you get airborne and close to the first altitude you'll be able to tweek the temperature as you get closer. Obviously carrying around a book with atmospheric tables and calculating your actual gross weight as a function of fuel burned will likely lead to an out-of-control helmut fire and mission failure.

So...make a spreadsheet in which you input your desired W/delta, your pre-takeoff gross weight, and starting fuel (gal). The spreadsheet needs to calculate the change in pressure altitude as a function of fuel burned for a given ambient temperature. To get temperature you can look up predicted values at altitude and print a few tables at different temps around the predicted or you can record ground OAT and use the -2 deg / thousand feet rule to predict the temp and print tables around that value.

Or you can load your spreadsheet on your ipad and simply input your fuel burned and get the new altitude point directly.

Also, for more accuracy you should add in your Ps corrections determined during your airspeed calculations - remember Ps also affects your Hi (indicated altitude).

The equation for Pa = Pssl * (1-(.0065*altitude/(Temp + 273.15)))^5.257
altitude = meters, Temp in celcius (do the conversions afterwards).

other equations:

delta = Pa/Pssl
Fuel Weight = 6.02 lbf/gal * Gal

I'll leave the math to you to solve in your spreadsheet or you can ask for mine and I'll email it to you.

If you fly at least 3 values of W/delta (1800/2000/2200) you can use linear regression to extrapolate the data to anywhere in the envelope with pretty good correlation - 3 runs total!!!

But for any speed mods you might have made you only need to refly any W/delta you flew prior to your mod and compare the data directly. This is really the best way to ensure you see improvements with any validity. Too often I read about folks making chagnes and reporting speed improvments without quantifying the method for capturing a true comparison of apples-apples.

I Hope this is helpful. Kkopp99 (at)

My head hurts - time for a beer!

Here is a copy of how it looks: (Hpo is Ps corrected Pressure altitude and the point you want to fly).

Fixed Wing Level Flight Performance - Weight/delta method

W/ς 2000 Wstart (lb) 1566.8
Fuel Start (gal) 42 Wcurrent (lb) 1551.8
Wempty (lb) 1124 ς 0.776
Wcrew (lb) 190 CAS (mph) 148

Predicted Fuel Used (gal) 2.5
OAT (deg F) 70 ς = Pa/Pssl
IAS (mph) 150 Pa = ς * Pssl

Hpo (ft) 6981 Hp (ft) 6997

Fuel Used (gal) W (lbf) ς Pa (lbf/ft^2) Hp (ft) Hpo (ft)
0 1566.8 0.783 1579 6737 6721
0.1 1566.2 0.783 1579 6747 6731
0.2 1565.6 0.783 1578 6758 6742
0.3 1565.0 0.783 1578 6768 6752
0.4 1564.4 0.782 1577 6778 6762
0.5 1563.8 0.782 1576 6789 6773
0.6 1563.2 0.782 1576 6799 6783
0.7 1562.6 0.781 1575 6809 6794
0.8 1562.0 0.781 1575 6820 6804
0.9 1561.4 0.781 1574 6830 6814
1 1560.8 0.780 1573 6841 6825
1.1 1560.2 0.780 1573 6851 6835
1.2 1559.6 0.780 1572 6861 6846
1.3 1559.0 0.780 1571 6872 6856
1.4 1558.4 0.779 1571 6882 6866
1.5 1557.8 0.779 1570 6893 6877
1.6 1557.2 0.779 1570 6903 6887
1.7 1556.6 0.778 1569 6913 6898
1.8 1556.0 0.778 1568 6924 6908
1.9 1555.4 0.778 1568 6934 6918
2 1554.8 0.777 1567 6945 6929
2.1 1554.2 0.777 1567 6955 6939
2.2 1553.6 0.777 1566 6966 6950
2.3 1553.0 0.776 1565 6976 6960
2.4 1552.4 0.776 1565 6986 6971
2.5 1551.8 0.776 1564 6997 6981
2.6 1551.2 0.776 1564 7007 6991
2.7 1550.6 0.775 1563 7018 7002
2.8 1550.0 0.775 1562 7028 7012
2.9 1549.4 0.775 1562 7039 7023
3 1548.8 0.774 1561 7049 7033
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Old 01-16-2012, 03:52 PM
fatherson fatherson is offline
Join Date: Oct 2009
Location: Albuquerque, NM
Posts: 414

Thank you for this, Ken. There are so many areas to learn about in this hobby, and it seems like the biggest holes are in FWF and in flight testing. The voices of experienced test pilots like you and experienced operations engineers like Paul have done much to expand the knowledge of the rest of us.

If I get some free time, I'm going to try coding up some of your post into an iOS app. It really may be more useful as a test to see if I understand rather than a useful tool, but I'll let you know if I make any progress.

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Old 01-16-2012, 04:49 PM
Bob Axsom Bob Axsom is offline
Join Date: Mar 2005
Posts: 5,685
Default I agree with the thought on the need for a baseline

I agree with the thought on the need for a baseline. The number on our airplane is 170.67 kts and the modifications we have made got us up to 184.4 kts. This is not the optimum speed etc. but from several years of testing I am confident that the test results are comparable and accurate within and acceptable error margin.

I fly three legs, at 6,000 ft D.alt.,WOT, leaned for best speed ROP, trimmed for hands off level flight, then apply autopilot to maintain direction and altitude control, allow the speed to settle, then record GPS ground speeds at 20 second intervals until I have 5 consecutive that do not vary outside of a 1kt envelope (start over on the leg record if you break out of the 1 kt envelope), then turn to the new heading and repeat until done, input the GPS track angles and the GPS ground speed average in each leg into the NTPS spread sheet and you will get a KTAS speed output that is a very good repeatable speed the you can record and and compare with other tests made using the same test method. Weight is not that big of a factor in level flight and if the airplane is reasonable close in weight (~100 pounds), I believe it can be disregarded in speed testing at our level of need to determine if a mod has produce positive or negative results. This is a relative measure but I believe it will yield a KTAS accurate to + 2 KTAS in the worst case.

Bob Axsom
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Old 01-17-2012, 06:51 AM
RBurn RBurn is offline
Join Date: Apr 2007
Location: Lexington Park, MD
Posts: 14
Default VIW vs PIW

Many times you will see rotary wing aircraft using W/sigma and turbine fixed wing aircraft using W/delta.

Another method not mentioned is VIW vs PIW. This stands for velocity independent of weight and power independent of weight. There is also NIW for fixed pitch props which is rpm independent of weight. These methods allow for correcting any weight, altitude, and airspeed to sea level performance conditions. Once the VIW vs PIW charts are made they can be "redeminsionilized" to specific altitudes and weights.

Two good texts are:
"Flight Testing of Fixed-Wing Aircraft," by Ralph Kimberlin
ISBN-10: 1563475642 | ISBN-13: 978-1563475641

"Introduction to Flight Test Engineering: Volume 1," by Ward, Strganac, and Niewoehner
ISBN-10: 0757529348

Kimberlin talks about NIW for fixed pitch props where Ward does not. Also, Kimberlin derives equations to plug in PIW and VIW and create drag polars with CD vs CL.

A basic knowledge of calculus is need to understand the derivations, but you only need to know basic algebra to do the data reduction.

Ron Burnette
Flight Test Engineer
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Old 01-17-2012, 10:23 AM
Kevin Horton's Avatar
Kevin Horton Kevin Horton is offline
Join Date: Jan 2005
Location: Ottawa, Canada
Posts: 2,071

I used the PIW & VIW method to reduce my cruise performance test data. The test points all day quite nicely on a straight line, except for two points just above stall speed.
Kevin Horton
Ottawa, Canada
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Old 01-17-2012, 12:14 PM
Bob Axsom Bob Axsom is offline
Join Date: Mar 2005
Posts: 5,685
Default Calculus

If you are interested in the books mentioned earlier and you feel put off by the need for a basic understanding of calculus maybe you shouldn't be. The book I used was written by Ross R. Middlemiss Professor of Applied Mathematics Washington University (maybe not so coincidently where I went to school). It is entitled "Differential and Integral Calculus" and it was published by McGraw Hill. My copy is the second edition published in 1946. It was clear and fairly easy to read and use. It was the current text used in my classes in 1972 so it is not a rapidly evolving subject as far as getting a basic understanding is concerned. In otherwords, someone with a desire and ability like one of my Canadian friends that self taught the IFR requirements and passed the written on the first try could pick up a text book on calculus and accuire enough understanding to comprehend the book reference earlier I'm sure. Otherwise I consider it a ...

Bob Axsom

Last edited by Bob Axsom : 01-17-2012 at 07:08 PM.
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