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) comcast.net
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
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) comcast.net
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