The One Hour Flight Test Program to Determine Aircraft Climb Performance

Bob Waldmiller

Originally published May 1993

When we left our story last time, Rocky and Bullwinkle were flying precariously close to powerlines and rising terrain in a Piper Cherokee 140 loaded to max gross weight with Aircraft Spruce Catalogs purchased at the Copperstate Fly-in. Having overestimated their aircraft's performance based on data presented in the operating manual means almost certain doom for our heroes. Little did they know that the manual had been written by the evilest of villains, Boris Badenov...aka..."I want to sell more airplanes so I'll fudge my performance numbers a bit--Piper."

"Look Boris, moose and squirrel are headed right at that mountain!"

"Yeah, isn't it wonderful Natasha, moose and squirrel will smack into mountain and we get Aircraft Spruce Catalogs for free."

As the picture looks more and more bleak, Rocky speaks the obvious. "I think the performance manual for this airplane was a little optimistic, Bullwinkle."

"I'll say! And in a few minutes we won't have much use for it either!"


Stay Tuned For...

Moose Modifies Mountain!

--OR--

Mountain Modifies Moose!


In a fit of panic, Bullwinkle tossed the operating manual out the window. Miraculously, the airplane started to climb which allowed our heroes to return safely home. However, in their next flight in the same airplane, Rocky and Bullwinkle found themselves in a similar situation 7500' MSL over the Mojave Desert. This time 120 lbs lighter, the airplane barely achieved a 200 ft/min rate of climb. Additionally, the engine was turning about 100 to 150 RPM less than required for the 75% power setting they desired.

"Boy, Rocky, this performance is depressing. Maybe if I work a little magic with the engine controls...Nothing up my sleeve...Presto!"

"What'd you get, Bullwinkle?"

"Oh, not much. Just this magazine...the Pacific Flyer--Swimsuit Edition."

"That's not what I mean, Bullwinkle. How's the engine?"

"Don't bother me now, Rocky, I'm reading..."

Does this mean their airplane will always have marginal high altitude performance or is there an unknown engine problem?

Given the above information, it appears that the engine is only producing 65% power rather than the desired 75% at wide open throttle. The first thing we'll do is give the engine a thorough inspection. Let's see, new spark plugs, new ignition harness, mag timing checked, cylinder differential pressure is in the mid 70s over 80 on all four cylinders, carb heat box rebuilt to replace a worn out seal and bushings, throttle plate moves to the fully open position, carb venturi looks ok, fuel and air filters all clean, and the mixture control operates normally. During run-ups the engine leans very smoothly like it always has, i.e. there is no engine shaking or backfiring as the engine is over-leaned which indicates to me that all four cylinders are getting pretty much the same mixture. Without the benefit of an EGT or a CHT it's difficult to be precise in my analysis, but I believe there are no defects in the engine itself. A tachometer check indicates that my tach is reading 50-60 RPM low throughout the entire operating range so I'm turning close to the required static RPMs although it's still 25 RPM low. Given the fact that we're 2300' above sea level while doing the run-up might have something to do with that however.

Now, what about the lack of climb performance? Time for the one hour flight test program! My objective is to learn as much as I can about the airplane's performance by doing a simple rate of climb check. Since I don't have calibration charts to correct for pitot-static system errors or instrument errors, I'll make the BIG assumption that the errors are reasonably small. Also, I presume Piper did a reasonable job of locating the pitot-static system on the airplane since certifying an airplane to Part 23 standards requires the airspeed system error to be within 3 percent or 5 kts--whichever is greater. Still, I'm making a BIG assumption here. To generate a little credibility however, I'll fly the airplane through a low speed ground course to verify my assumptions. 'Nuff said about instrument errors.

The procedure is simple. After setting the altimeter to 29.92, I'll climb at the best rate of climb speed (85 mph) from 500' AGL to 8000' pressure altitude. At 500 foot increments, I'll note the total elapsed time on the stopwatch (starting from a reference altitude) and the outside air temperature. During the climb, I'll keep adjusting the mixture to achieve best power on the engine and all the while, the throttle will be wide open. Simple, huh?


...I'll be back in an hour, it's time to fly...

Still with me? Great! Before I started my climb, I performed an airspeed calibration test by flying both ways through a 4 mile ground course. The first two runs were done at 80 mph indicated in both directions and the second two runs were done at 85 mph indicated. A few minutes of electronic whiz-wheel time to calculate the average ground speed through the course along with my true airspeed revealed that my total airspeed system errors are less than 1 mph at both 80 and 85 mph! That's fantastic! How'd Piper do that?

Ok, back to the rate of climb data. I took the liberty and already did some number crunching in order to correct my data to standard atmosphere conditions. In addition, I calculated the actual rate of climb (ROCact) for each altitude based on the corrected altitudes and the stopwatch timing values. Since there is some scatter in the data due to vertical air mass movement during the test flight and altimeter errors, I applied a linear regression fit to the ROCactdata to smooth it out (ROClr). Finally, I determined the horsepower required to climb at those rates using the following equation:

HPclimb = ROC * Wt / 33000

Where ROC is the rate of climb in feet/minute and Wt is the aircraft weight in pounds. Table 1 is a summary of the raw flight test data and the calculated data.

RAW DATA
CORRECTED/CALCULATED DATA
P-Alt
Time
Temp C
RPM
Std Alt
TAS
delta t sec
ROCact
ROClr
HPclimb
HPavail
HPdrag
---
---
---
---
0
85.0
---
---
1020
51.6
108.8
57.2
3000
0
19
2390
4011
90.3
XXX
XXX
---
---
---
---
3500
1:04.16
19
2370
4621
91.1
64.16
514
643
32.5
---
57.2
4000
2:15.70
18.5
2397
5174
91.9
71.54
515
598
30.3
---
57.2
4500
3:12.59
18
2400
5728
92.7
56.89
670
552
27.9
---
57.2
5000
3:59.73
18
2380
6337
93.5
47.14
612
503
25.5
---
57.2
5500
5:09.80
17.8
2390
6923
94.4
70.07
508
455
23.0
---
57.2
6000
6:23.51
18
2390
7554
95.3
73.71
478
403
20.4
77.6
57.2
6500
7:42.48
17.8
2385
8139
96.1
78.97
394
356
18.0
---
57.2
6500
7:42.48
17.8
2385
8139
96.1
78.97
394
356
18.0
---
57.2
7000
8:54.85
16
2376
8547
96.7
72.37
224
322
16.3
---
57.2
7500
10:59.86
13.5
2385
8876
97.2
125.01
215
296
15.0
---
57.2
8000
12:29.12
12
2372
9316
97.9
89.26
280
260
13.2
---
57.2
8500
14:08.14
10.5
2370
9756
98.6
99.02
182
224
11.3
---
57.2
9000
17:20.00
9
2370
10196
99.3
191.86
215
188
9.5
---
57.2
9500
18:30.00
8
2375
10693
100.0
70.00
139
147
7.4
---
57.2
10000
23:39.00
6
2325
11076
100.6
309.00
XXX
---
---
---
---
Airspeed = 85 mph indicated (instrument & position error < 1 mph)
Aircraft weight = 1670 lbs
Table 1

Since the purpose of this exercise is to determine what the aircraft performance will be at 2150 pounds (gross weight) and compare it with the data that Piper published, I need to determine how much horsepower is consumed by aircraft drag in the climb configuration. Unfortunately, I can't measure drag directly nor do I know how much thrust the propeller is generating to measure it indirectly. Therefore, I'm forced to make a few more assumptions...oh, oh, there's that word again! Conservatively, those assumptions are:

  1. The engine produces 150 HP at sea level at 2700 RPM and 75% power at 7500' at 2600 RPM (per the operating manual).
  2. The engine power output varies linearly with RPM from 2300 RPM to 2700 RPM.
  3. The propeller efficiency is 75% and is constant with altitude, RPM, and true airspeed. This is not entirely true. However, changes should be relatively small and in fact will probably fall to something less than 75 percent at the higher true airspeeds. Therefore this assumption is very conservative.
  4. The airframe parasitic drag is constant at 85 mph indicated in the climb configuration and only the induced drag will vary with aircraft weight. This is a good assumption until reaching the higher Mach numbers. (Come on now...high Mach numbers in a Cherokee???)

First, I'll need to determine how much available horsepower I have at 75% power at 7500' standard altitude. From Table 1 we see that the engine is turning 2390 RPM at approximately 7554 feet standard altitude. From the above assumptions we defined the propeller efficiency as 75 percent and the desired RPM as 2600. So using the following equation,

HPavail = 150 * n * RPM/2600

we find that HPavail = 77.6 HP. From that we can subtract HPclimb at 7554 feet standard altitude (20.4 HP) to get the horsepower required just to overcome the aircraft drag (HPdrag) which is 57.2 HP. Now, according to the fourth assumption, HPdrag is not dependent on altitude which allows us to do a quick check at sea level values. Adding HPclimb and HPdrag together gives 108.8 for HPavail at sea level. Since I can only get about 2450 RPM at sea level at 85 mph, the HPavail should only be 102.1 HP. Between the errors in the curve fit and my assumptions, I deem this 6.7 HP error acceptable.

The next step is to determine how much more horsepower I must give up at the higher gross weight to overcome the additional induced drag. To determine that, I must first calculate the lift coefficient at both weights. Using the well known formula,

CL = (2 * W)/(rho * V**2 * S)

out pops the two numbers of CL 1670 = .603 for the 1670 pound airplane and CL 2150 = .776 for the 2150 pound airplane. (Oh, by the way, S = 150 ft2, V = 124.7 ft/sec, and rho = .0023769 slug/ft3.) The change in the induced drag coefficient can be expressed as follows:

Delta CDi = (CL(2150)**2 - CL(1670)**2)/(PI * e * AR)

Where e = Oswald's Efficiency factor of 0.8 for a rectangular wing, and AR is the wing's aspect ratio of 6. The result is a change in the induced drag coefficient of 0.0158 which doesn't sound like very much but when expressed as a change in horsepower,

Delta HPdrag = (rho * V**3 * Delta CDi * S)/(2*550)

it works out to 9.9 horsepower, which is very significant! By adding this 9.9 HP to each HPdrag term, which in turn means there's 9.9 fewer HP for each HPclimb term, we can calculate a rate of climb value for each altitude for the higher gross weight. Table 2 is a summary of that data.

CALCULATED/PREDICTED DATA
Std Alt
TAS
HPavail
HPdrag
HPclimb
ROClr
0
85.0
108.8
67.1
41.7
640
4011
90.3
---
---
---
---
4621
91.1
---
67.1
22.6
347
5174
91.9
---
67.1
20.4
313
5728
92.7
---
67.1
18.0
276
6337
93.5
---
67.1
15.6
239
6923
94.4
---
67.1
13.1
201
7554
95.3
77.6
67.1
10.5
161
8139
96.1
---
67.1
8.1
124
8547
96.7
---
67.1
6.4
98
8876
97.2
---
67.1
5.1
78
9316
97.9
---
67.1
3.3
51
9756
98.6
---
67.1
1.4
21
10196
99.3
---
67.1
-0.4
-6
10693
100.0
---
67.1
-2.5
-38
11076
100.6
---
---
---
---
Aircraft weight = 2150 lbs
Table 2

After all this work, we can finally show all the relevant data in a single graph. Figure 1 allows us to see the original flight test data at 1670 lbs, the linear regression curve fit applied to this data, the predicted data at 2150 lbs gross weight, and Piper Aircraft's data for a 2150 lb airplane as published in the operating manual.

Rate of Climb Results

Figure 1

So what conclusion can we draw from all this? Well, for starters, more test data at lower altitudes would improve the curve fit and would most likely change the slope of the lines a bit. Secondly, the gross difference between my predicted data and Piper's would indicate that Piper's test aircraft could produce more useable climb power at altitude than mine can. The only way this could be possible would be to either reduce the aircraft drag at high altitudes or increase the propeller efficiency with altitude. The first explanation isn't possible without changing the aircraft configuration, and the second explanation requires some really dramatic changes in propeller efficiency--like 75 percent at sea level to 91 percent at 16500 feet (Piper's estimated service ceiling for the Cherokee 140)! I even gave Piper the benefit of the doubt by allowing them to use a climb prop to generate their rate of climb chart and I used their power charts as well. One last point. In Piper's Operating Manual, the rate of climb chart for the Cherokee 140 has the same slope as the Cherokee 180 except that it's offset 75 ft/min lower. This difference might be valid at sea level but by the time both aircraft reach 7500 feet, the difference should be at least 250 ft/min in favor of the Cherokee 180. And this is using Piper's own data!!! Guess what? Applying these corrections to the operating manual gives almost the same rate of climb data which I predicted in the above analysis!

My conclusion is that N554FL is pretty healthy for a 22 year-old airplane. Also, the data in the operating manual is correct only for the Cherokee 180 and Piper pushed a lot of B.S. into the manual for the Cherokee 140! Where's my waders??? The question I'm sure you've been dying to ask is: Why didn't I just load up the airplane to 2150 lbs gross weight and get all my test data there--and avoid all the mathematics? Boy, am I glad you asked that. The answer is: Because I didn't know if it was the engine or the operating manual which was faulty. If indeed I had an engine problem, its effects were undocumented. By flying at the lighter weight, I could approach the problem more safely. The next step is, of course, to verify my predictions by flying the test flight again at 2150 lbs.

You may even wish to duplicate this test in your own airplane for the purpose of documenting its rate of climb performance. There's no substitute to having good data--ask anyone who flew with me at last year's Copperstate Fly-In!

I Can Fly?

by: Bullwinkle the Moose

Today I wished to fly real high;
Thirteen thousand feet in the sky.
Play with the clouds, that was my goal.
Here we go now, the takeoff roll.

But in a Piper Cherokee;
There isn't any energy.
The rate of climb is very low;
Beanstalks won't even grow that slow.

It flies much better when it's light;
Ask the squirrel, you know he's right.
He'll also tell you, all about flying;
That moose really can't, and shouldn't be trying.

"Hey, who put that in there?"
"Never mind, Bullwinkle."

** end **

Check out the Sequel "Frostbite Falls Flyer Foils Foul Fossil Fueled Fallacy"


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Revised -- 22 February 1997