Tachyon1000

01-06-2006, 03:44 PM

Level Acceleration Performance Tests

Intro

In an effort to derive a climb schedule via techniques actually used for that purpose, I performed level acceleration tests to determine the specific excess power that may be used to determine best rate of climb. In the modern total energy perspective of flight theory it is known that power for acceleration or power for climb are essentially the two aspects of the same thing, a balance of kinetic and potential energy derived from lift and engine power and that of drag. Therefore one can merely fly level at a specific altitude and a specific power setting and determine the maximum specific excess power and the speed associated with it.

The total energy state of the aircraft is merely the sum of its potential and kinetic energy. Specific excess power is merely the derivative of the total energy state with respect to time. The power is excess in that it is power in excess of that needed for level flight or merely more than drag on the airplane. The conceptual formula is simple:

Ps = dh/dt + (Vt/g)(dVt/dt)

where Ps is specific excess power in ft/sec, h is altitude in feet, Vt is true airspeed in ft/sec, and g is the gravitational acceleration constant (32.3 ft/sec^2).

Any specific excess power determined via level acceleration tests is true only for the specific conditions it was tested under, i.e. altitude, temperature, weight, thrust, etc., however an adjustment can be made for other weight conditions.

The specific excess power is directly translatable into rate of climb and maximum Ps is the same as best ROC for the specific altitude and speed.

More detailed info on theory and procedures can be found here:

http://flighttest.navair.navy.mil/unrestricted/FTM108/c5.pdf

http://www.dfrc.nasa.gov/Education/OnlineEd/Intro2Flight/nasaccel.html

Procedure

Missions were created in FMB for target test altitude. I used Crimea map, P-38J, 75% fuel, 54€ of manifold pressure, auto radiator. Basically, the procedure is to establish level flight for target altitude at the lowest power setting needed for level flight and add throttle to desired level (here 54€ MP), and maintain level flight within 300ft of target altitude. Data collected with UDPGraph was IAS, TAS, MP, altitude, and time between readings. Poll time for UDPGraph was set at 500msec. Inputs (dh/dt and dVt) to the Ps equation were estimated via the difference between altitude and TAS between data collection intervals divided by the poll interval recorded by UDPGraph. I ran at least four trials for altitudes of 10,000, 15,000, 20,000 and 25,000 ft. None for 35,000 ft as the P-38J cannot maintain correct manifold pressure at this altitude, and only 1 trial of 5,000 ft as climb performance is not terribly at issue at this altitude.

Results:

Mean results of the tests are as follows:

5,000 ft ROC = 3068.21 ft/min IAS = 182.93 mph

10,000 ft ROC = 2843.04 ft/min Weight Adjusted ROC = 2900 ft/min

IAS = 176.01 mph

15,000 ft ROC = 2696.1 ft/min Weigh Adjusted ROC = 2771.60 ft/min

IAS = 167.73 mph

20,000 ft ROC = 2523.9 ft/min Weight Adjusted ROC = 2607.19 ft/min

IAS = 158.02 mph

25,000 ft ROC = 2201.55 ft/min Weight Adjusted ROC = 2274.2 ft/min

IAS = 146.55 mph

To explain the weight correction, Ps and thus the ROC were determined for a plane of 75% fuel weight, however the pilots€ manual shows fuel used to obtain the altitude, thus the plane is lighter at higher altitudes. I determined a weight for a P38L with 75% fuel with a base weight of 14,400 lbs + 6.5 pounds per gallon of fuel indicated by UDPGraph for 75% fuel, that weight being 16318.4 lbs. To determine the weight that the plane would be as per the pilots€ manual climb schedule I merely subtracted a weight equal to the weight of fuel used in the chart from the weight for the plane at 75% fuel. Weight Adjusted Ps was then determined by a simple proportional relation:

the calculated Ps/the 75% fuel plane weight = the weight adjusted Ps/the weight that the plane should be as per the climb schedule.

http://www.geocities.com/grantsenn/NACA_TESTING/P38/WR_GCS00001/FIG01.jpg

Fuel usage is given by the above chart.

Below is a ROC curve that TAGERT has presented elsewhere. It claims to give rates of climb for the indicated altitudes for a P-38J climbing optimally at 54 inches of manifold pressure (curve labeled 54€ Pilots Manual Data). The curve labeled €œin-game DeviceLink Data€ is from TAGERT€s own test data, not mine.

http://i32.photobucket.com/albums/d35/ivankautter/P38J_ROC_TAGERT.jpg

Interpolating from this graph, we arrive at these ROC values for the following altitudes from the Pilots Manual Data:

5,000 ft ROC = 3000 ft/min

10,000 ft ROC = 2750 ft/min

15,000 ft ROC = 2600 ft/min

20,000 ft ROC = 2400 ft/min

25,000 ft ROC = 2050 ft/min

Comparing these interpolated values to those obtained in the level acceleration tests, we can see that the P-38J at 54€ MAP in-game actually exceeds what I am assuming is the real world performance of the P-38J.

Conclusion:

The P-38J meets or exceeds the interpolated values from the graph above that TAGERT has referenced as a conservative estimate of the climb performance of the P-38J during the climb check. This is an independent confirmation of the flight performance of the J that is not dependent upon the performance of the pilot in the climb check.

Intro

In an effort to derive a climb schedule via techniques actually used for that purpose, I performed level acceleration tests to determine the specific excess power that may be used to determine best rate of climb. In the modern total energy perspective of flight theory it is known that power for acceleration or power for climb are essentially the two aspects of the same thing, a balance of kinetic and potential energy derived from lift and engine power and that of drag. Therefore one can merely fly level at a specific altitude and a specific power setting and determine the maximum specific excess power and the speed associated with it.

The total energy state of the aircraft is merely the sum of its potential and kinetic energy. Specific excess power is merely the derivative of the total energy state with respect to time. The power is excess in that it is power in excess of that needed for level flight or merely more than drag on the airplane. The conceptual formula is simple:

Ps = dh/dt + (Vt/g)(dVt/dt)

where Ps is specific excess power in ft/sec, h is altitude in feet, Vt is true airspeed in ft/sec, and g is the gravitational acceleration constant (32.3 ft/sec^2).

Any specific excess power determined via level acceleration tests is true only for the specific conditions it was tested under, i.e. altitude, temperature, weight, thrust, etc., however an adjustment can be made for other weight conditions.

The specific excess power is directly translatable into rate of climb and maximum Ps is the same as best ROC for the specific altitude and speed.

More detailed info on theory and procedures can be found here:

http://flighttest.navair.navy.mil/unrestricted/FTM108/c5.pdf

http://www.dfrc.nasa.gov/Education/OnlineEd/Intro2Flight/nasaccel.html

Procedure

Missions were created in FMB for target test altitude. I used Crimea map, P-38J, 75% fuel, 54€ of manifold pressure, auto radiator. Basically, the procedure is to establish level flight for target altitude at the lowest power setting needed for level flight and add throttle to desired level (here 54€ MP), and maintain level flight within 300ft of target altitude. Data collected with UDPGraph was IAS, TAS, MP, altitude, and time between readings. Poll time for UDPGraph was set at 500msec. Inputs (dh/dt and dVt) to the Ps equation were estimated via the difference between altitude and TAS between data collection intervals divided by the poll interval recorded by UDPGraph. I ran at least four trials for altitudes of 10,000, 15,000, 20,000 and 25,000 ft. None for 35,000 ft as the P-38J cannot maintain correct manifold pressure at this altitude, and only 1 trial of 5,000 ft as climb performance is not terribly at issue at this altitude.

Results:

Mean results of the tests are as follows:

5,000 ft ROC = 3068.21 ft/min IAS = 182.93 mph

10,000 ft ROC = 2843.04 ft/min Weight Adjusted ROC = 2900 ft/min

IAS = 176.01 mph

15,000 ft ROC = 2696.1 ft/min Weigh Adjusted ROC = 2771.60 ft/min

IAS = 167.73 mph

20,000 ft ROC = 2523.9 ft/min Weight Adjusted ROC = 2607.19 ft/min

IAS = 158.02 mph

25,000 ft ROC = 2201.55 ft/min Weight Adjusted ROC = 2274.2 ft/min

IAS = 146.55 mph

To explain the weight correction, Ps and thus the ROC were determined for a plane of 75% fuel weight, however the pilots€ manual shows fuel used to obtain the altitude, thus the plane is lighter at higher altitudes. I determined a weight for a P38L with 75% fuel with a base weight of 14,400 lbs + 6.5 pounds per gallon of fuel indicated by UDPGraph for 75% fuel, that weight being 16318.4 lbs. To determine the weight that the plane would be as per the pilots€ manual climb schedule I merely subtracted a weight equal to the weight of fuel used in the chart from the weight for the plane at 75% fuel. Weight Adjusted Ps was then determined by a simple proportional relation:

the calculated Ps/the 75% fuel plane weight = the weight adjusted Ps/the weight that the plane should be as per the climb schedule.

http://www.geocities.com/grantsenn/NACA_TESTING/P38/WR_GCS00001/FIG01.jpg

Fuel usage is given by the above chart.

Below is a ROC curve that TAGERT has presented elsewhere. It claims to give rates of climb for the indicated altitudes for a P-38J climbing optimally at 54 inches of manifold pressure (curve labeled 54€ Pilots Manual Data). The curve labeled €œin-game DeviceLink Data€ is from TAGERT€s own test data, not mine.

http://i32.photobucket.com/albums/d35/ivankautter/P38J_ROC_TAGERT.jpg

Interpolating from this graph, we arrive at these ROC values for the following altitudes from the Pilots Manual Data:

5,000 ft ROC = 3000 ft/min

10,000 ft ROC = 2750 ft/min

15,000 ft ROC = 2600 ft/min

20,000 ft ROC = 2400 ft/min

25,000 ft ROC = 2050 ft/min

Comparing these interpolated values to those obtained in the level acceleration tests, we can see that the P-38J at 54€ MAP in-game actually exceeds what I am assuming is the real world performance of the P-38J.

Conclusion:

The P-38J meets or exceeds the interpolated values from the graph above that TAGERT has referenced as a conservative estimate of the climb performance of the P-38J during the climb check. This is an independent confirmation of the flight performance of the J that is not dependent upon the performance of the pilot in the climb check.