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Power and Drag for the Common Man

New perspectives, techniques, and a working model

By Howard Handelman, EAA 111399, EAA_article@n6zb.info

My plane is too slow—is it too little power or too much drag?
What is my propulsive efficiency?
How does my plane’s efficiency compare to that of my buddy’s plane?
How will changing weight affect performance?
What will my fuel consumption be at x speed and altitude?
What is the best engine-out speed in a head wind?
Why is the best glide for engine-out different than for the drag curve?
How much prop drag is there with the engine stopped or windmilling?
Why does my best glide speed take more power than my minimum sink speed?
How can I find my best glide speed and ratio?
How can I know which of my test-flight observations are suspect?

These and other questions can be answered with this model, a simple, direct, valid, and reasonably consistent way of testing and predicting some important airframe characteristics. Any of us can do it with commonly available instruments, probably already installed in your plane. A second, equally important benefit: it allows us to judge whether our test data conform to the model or how far out they are. This can improve testing.
This article explains the use of the model, which is built into this Excel* spreadsheet.

Model Picture

Model Picture

The drag curves (and thus power curves) always have the same mathematical shapes, and so do their combined curves. The shapes can easily be expressed as formulas and graphed. Therefore, if you can find two defined points, you can compute any other points. You can place your airplane on the x-axis by its best L/D (lift-drag ratio)  speed and on the y-axis with your minimum drag. I set out to exploit this knowledge for use in experimenting with and improving my RV-7A. I learned so much that I decided to share it with others who are interested. While nothing in this model is actually new, it’s a newly integrated view of what is already well-known, giving us new methods and perspectives.
Although I have worked very hard to get this right, I have no doubt that I’ve made some mistakes. Feel free to point them out. I’m neither a mathematician nor an engineer. I’ve had some patient and generous help from Kevin Horton, a very qualified engineer test pilot, developing and checking this model, but any errors are mine. Kevin prepared the spreadsheet page that bears his name and against which my or your results can be compared. Kevin has not approved this (yet), but I am working on him! I also thank Jack Norris for sharing his insights. Again, all the errors are mine, and no endorsements are implied.

TABLE OF CONTENTS

  • Existing Problems
  • Premises and Deductions
  • Different Methods of Placing Your Aircraft on the Drag Curve in the Model
  • Building and Using the Model
  • In Practice
  • Additional Discoveries
  • Findings and Conclusions
  • CAFE Measurements
  • Next Steps
  • Detailed Premises and Deductions

1. EXISTING PROBLEMS
Testing airframe efficiency (lift, drag, glide, sink, etc.) can be very difficult, and yet after best efforts with advanced technology, highly skilled test pilots, and talented engineers, results may have undesirable margins of error. This can be seen in some CAFE Foundation (Comparative Aircraft Flight Efficiency) reports such as the RV-6A.

Also, when testing the performance of the airframe we often have difficulty in factoring out the differences in the power system either in glide or at top speed. Power required is not easily determined from engine observations. With a new experimental aircraft in phase one, quickly and exactly finding the V speeds  is important, but it’s time-consuming and error-prone due to the changing conditions of test flights. Best L/D (best lift over drag, or VLD) is especially important, and previously there was no accurate method of directly determining it; it required iterations and calculations while conditions could change. This model’s methods offer a more direct way using newer instruments—angle of attack (AOA) and GPS.

2. PREMISES AND DEDUCTIONS
The detailed premises and deductions can be read at the end of the article. They are the heart of this model, but you don’t need them to use the spreadsheet and methods.

The first and most important premise is this: If test results do not conform to the model, then at least one measurement is in need of correction. That’s essential. When data and model disagree, at least some of the data are wrong. For example, if your data when used in this model cannot correctly predict your fuel flow at a given speed and altitude, then at least one factor needs adjustment. All applicable test data should be reviewed with the model.

Model Flow Chart

3. DIFFERENT METHODS OF PLACING YOUR AIRCRAFT ON THE DRAG DIFFERENT METHODS OF PLACING YOUR AIRCRAFT ON THE DRAG CURVE IN THE MODEL
“Method X”: For all methods listed below, first find the CAS  (calibrated airspeed) for VLD and VMS (minimum sink). This places your drag curve on the x-axis.

  • Measure thrust horsepower (THP) using sink (or climb) rate and fuel flow or speed change (best).
  • Measure brake horsepower (BHP) by inference from fuel flow at several speeds (easiest)
  • Find sink rate at VMS or sink rate at VLD with engine off (not recommended).

Note: All of these methods distinguish between calibrated airspeed and true airspeed (TAS). In layman’s terms (not the strict definition), CAS is what your airspeed indicator should read (indicated) when your TAS is reverse-engineered for density altitude (DA). In other words, if your TAS is 150 (knots or mph) and your DA is 8,000 feet, plugging these numbers into your trusty E-6B flight calculator will give you a CAS of about 132.5. We usually work in the opposite direction (using CAS to determine TAS), but this reverse method is useful for testing because TAS can be determined easily with a GPS, and CAS is very hard to measure directly without exotic instrumentation like those used by CAFE.

Put another way, you can easily find TAS with a GPS. Once TAS is determined, an E-6B can be used to find CAS. If your airspeed indicator (ASI)  doesn’t read this number, then the installation needs to be altered, or some other form of conversion needs to be made. Also see the accompanying article in this issue, “How Fast Are You Really Going? ” by Paul Lipps.—Pat 

You need accurate OAT (outside air temperature) and altimeter to find density altitude. Your trusty E-6B can be used to find CAS from TAS. Below 10,000 mean sea level (MSL), the model provides a more precise conversion. Most of the recommended methods also require fuel flow. Note further that equivalent airspeed  (EAS) is ignored here because of its negligible effect at RV speeds and altitudes below 10,000 MSL.

How to Find Speeds for VLD and VMS
The old way is iterative, depends on handmade graphs, and is both difficult and sloppy. The entire series of 196 through 496 Garmin handheld GPS units have a data field available for “Glide Ratio.” That’s the best tool to use. Theory and practice agree that at a range of power settings, the best glide will be at the same angle of attack that for a given weight and atmosphere is the same as saying “at the same IAS.” You don’t have to turn off the engine. You can use a power setting that gives you a 300-500 foot/minute descent. Note: The power used must be less than required for VMS in level flight for this to work.

If your airplane is type certificated and the manufacturer provides a speed for best glide, it is almost certainly different than what this method will yield. The weight for the manufacturer’s speed is almost always gross weight. We can correct for that, and it’s built into the spreadsheet; however, the manufacturer’s speed is usually given with the engine off and prop windmilling, and that almost certainly has more drag than this power-on method, which should approximate the CAFE zero thrust method (ZT).

Vary the IAS with pitch only (hold power constant) so that the number in the glide ratio field is highest. I found this worked best when the ratio was around 25 or 30, but that’s just personal preference. Just pick a power setting (preferably low) and vary airspeed with pitch. The best L/D speed (VLD) for that weight is now known, and 76 percent of that is your minimum sink (VMS) speed.

Please note that strong head or tail wind components will affect your search for this speed. Although conventional wisdom says that we should speed up when gliding into a head wind and slow down for a tail wind, when the drag curve is taken into account, the variation in best speeds when the wind vector on the nose or tail is less than 25 percent is less than 4 percent. That said, for best accuracy, the wind must be neutral. A mild crosswind is preferable to a head wind or a tail wind. You can cross-check your VMS finding by flying your airplane level at the slowest speed that does not require you to add power (working your way from faster to slower). That will be VMS.

Enter the best VLD (CAS mph) in the model’s “Start Here” page. Enter the weight for this test in the model on the same page.

Why Method C Is Not Recommended and Method A, Version 2 Is Best
We always need to compare alike things—apples to apples if you will. CAFE solved this problem with its zero thrust (ZT) device and method. CAFE created a device that when attached to the engine, can sense crankshaft end-play and determine when the crank is not being pulled or pushed by the propeller. Only with an approach such as this, which removes prop drag completely from the measurements, can we get consistent results. A side benefit is that we can isolate and measure the contribution of the prop.

Since the ZT device is a major effort, I sought a way to get a similar result without a device. If you turn off the engine, you get prop drag, so that is why Method C is not the best way (nor is it as safe). Methods that use gravity apply that constant to measure its effect and are thus reliable and repeatable.

The goal of CAFE’s ZT and my methods A and B is to make the prop transparent. Since we cannot eliminate prop wash effects, neither can be perfect but all three are close. ZT eliminates prop thrust and drag, while A and B work with thrust changes and gravity.

Both my methods A and B (except Method A, Version 2) use fuel flow. Method A also uses gravity and measures THP , but Method B infers BHP from THP, BSFC  (brake specific fuel consumption), and propulsive losses where BSFC and propulsive losses are estimated or deduced. From this you will conclude that this model is not very useful for evaluating actual engine-out glide distances. That’s mostly correct. Even using propulsive efficiency or losses tells us nothing about prop drag, either stopped or windmilling. Only Method C includes prop drag. The good news is that comparing the results of Method C to the other methods will allow a measurement of prop drag.

Method A
Measure THP using gravity (sink or climb) and fuel flow and/or speed change (best). Version 1 of this method subtracts a measured fraction of the power for level flight and observes the resulting sink rate. The proportion of power subtracted is multiplied by the THP change that was calculated from the sink rate and weight [sink_fpm x weight / 33,000 = THP]. Obviously, this requires holding IAS constant, and using trim is recommended as a technique. You will need to accurately convert IAS to TAS. It can be hard to fly well.

Version 2 of this method uses constant power, adds gravity, and computes THP change from sink (as above) combined with TAS change. This method works for fixed-pitch or constant-speed props and doesn’t require a fuel flow reading. However, it can be even harder to fly precisely.
An added challenge in flying them is that these two methods, in order to be reasonably accurate, must be accomplished in a small range of altitudes.
Version 1 example: You are cruising level at 180 mph TAS using 7 gallons per hour (gph). Reduce fuel flow by 1 gph (1/7) while holding pitch (airspeed) and exhaust gas temperature (EGT) constant. Observe sink rate. In this example, to compute the THP change, multiply by 7. What we’re after is a change in fuel flow at the same BSFC, such that the plane will sink because gravity must replace power to maintain airspeed. The degree to which gravity replaces power can be measured by the sink rate times the weight, and the degree of power reduction is the fraction by which you reduced fuel flow with throttle. So in this example, we reduced power via throttle by 1/7, then you can multiply the THP change due to gravity by 7 to get the THP for level flight. Seven and 1/7 are merely convenient values for the example; the spreadsheet can handle any reasonable fraction.
If you prefer to let the model do the work, just use the “Start Here & Method A” page and enter your numbers. It will solve for the sink rate at VLD mph TAS and other stuff, too. The results can be transferred to the page for your airplane’s performance. CAFE’s RV-6A data is there, both versions, for illustration.

If you want to get your hands dirty, mathematically speaking, compute the THP change: If you get a sink rate of 300 fpm for a 1,600-pound airplane, the THP change is [300 x 1600 / 33,000 = 14.5]. Since you subtracted 1/7 of the fuel flow, your power for level flight is [7 x 14.5 = 101.8 THP]. THP is defined as [TAS x foot_ factor / 60 x drag / 33,000], so now we also know the drag for level flight at this speed. Foot_ factor is 5,280 for miles or 6,076 for knots. You can now iteratively vary the VLD sink rate in the model until the THP at 180 TAS equals 101.5. Further, you can now experiment with the constants for propulsive efficiency and BSFC to see what might get you 7.0 gph and still be reasonable. It all has to tie together with reality.

This version (Method A, Version 1) can also be used with climb instead of sink. Instead of subtracting fuel flow (power), add it. Instead of sink rate you will see a climb rate. The same math applies. The same requirement for holding BSFC and TAS constant also applies. Use a negative number for fuel flow change and for sink rate on the “Start Here & Method A” page if you are using climb.

The accuracy of this method does not depend on the value of BSFC (just its consistency) or on propulsive efficiency, only on the accuracy of fuel flow, DA, TAS, and sink or climb rate (use GPS). This method can and should be used at a few different speeds. Running lean of peak (LOP) is preferred but not necessary. But, maintaining the BSFC equal during the test is critical, so EGT should be used. The model uses TAS. It would be best to do the test at the lowest practical altitude and the same altitude (or rpm if you have a constant-speed prop) for a series of speeds. See notes about Cessna data below for the reason why.

In my own testing I noticed my RV would cycle (bob) for a while when power was reduced before the sink rate steadied. Once you know the rate to expect, you can use small pitch inputs to reduce or eliminate this delay. This is normal aircraft behavior. If you let it go too long, you will wind up at a different altitude sufficient enough to affect accuracy through change in engine performance due to DA.

Method A, Version 2
Establish a medium speed level cruise, note DA (or pressure altitude and temp) and TAS. Without changing power, push (trim) the nose down, allowing speed to increase. In my trials I found that a 300-500 foot/minute descent works well. Stabilize the new airspeed and sink, then note both as well as the new DA. Fill in the yellow fields in the “second block” on the “Start Here” page of the spreadsheet. It will compute  the two decimals that those speeds’ THPs are of the THP for VLD speed. It will subtract. The difference will be a decimal value less than one. It computes the THP that gravity added [weight x sink / 33,000]. It divides that THP by the difference to get the THP for VLD speed TAS mph. It computes the sink at VLD by dividing the observed sink by the difference. Enter it into the “My Plane” page. There is a possible accuracy issue with this method in that power may increase due to the higher speed and the increasing air density. For now, the method does not handle that.

Method B
Measure BHP by inference from fuel flow at several speeds and find sink rate(s). For this, as with Method A, Version 1, you will need an accurate fuel flow instrument and all-cylinder EGT. Then you should learn to operate lean of peak (LOP). This is because fuel flow varies directly with BHP when operating LOP. According to the experts at General Aviation Modifications Inc., maker of GAMI injectors, a normal Lycoming-type fuel-injected aircraft engine in good condition (compression ratio 8.5-to-1) uses about 0.40 pounds of fuel per horsepower per hour when EGTs read 50°F lean of the peak reading. In other words, 0.40 BSFC. There will be some difference for other engines and compression ratios. Now that you are ready, fly the airplane at VMS, VLD, and Carson’s speeds , and perhaps at high cruise, noting the fuel flow at each. If you have a carburetor or don’t want to use LOP, you can use a best-power mixture as inferred from EGT 50°F or 75°F rich of peak and use a different BSFC if your engine manufacturer has said what it is. A BSFC of 0.50 or 0.051 is typical for best power for most air-cooled four-stroke piston engines. Superior Air Parts Inc., the world’s leading manufacturer of FAA-approved replacement parts for Lycoming and Continental aircraft engines, for example, says that for its XP-360 at EGT peak, BSFC is 0.43 and best power is 0.48. Use what works for you.

The problem with using fuel flow, even assuming that your BSFC is correct, is the propulsive efficiency is unknown and is not a constant throughout the speed range. However, in my testing, using 85 percent for propulsive efficiency, the error seemed pretty small. In a study of the C-152 it was significant. If you combine this method with Method A, Version 2, you will have a way to closely estimate your propulsive efficiency. Craig Catto of Catto Propellers told me that the efficiency of his props is not constant but is so close that it can be used effectively here. I have not confirmed this, and it may be different for constant-speed props or other fixed-pitch props. When comparing data between methods A and B it was necessary to change my propulsive efficiency to 85 percent to match predicted results to actual ones. This illustrates a value of the model. While not exact or directly measured, the envelope within which your estimates must fall will be very small.

Enter the constant factors for BSFC and propeller efficiency into the model. If you used Method A first, you have estimates available.
Using your observations, you now have several fuel flow measurements at various true airspeeds. Find those speeds on the “My Plane” page, then compare and adjust sink rate at VLD CAS mph (which adjusts minimum drag) to fit.

I’ve analyzed the pilot’s operating handbook from the C-172 from 1959 and 1978, the C-150 (1977) and the C-152 and found that altitude or rpm appear to affect propulsive efficiency, and the difference can be as much as 66 vs. 80. Therefore I suggest that you use the lowest feasible altitude for these measurements and keep it the same for each set of measurements. With this method, you can just enter trial values for the sink rate at VLD CAS mph until the model’s fuel flow values are very close to your observed values. If it works for you as it did for me, you will find all three methods will agree closely and with theory when you find the right sink rate.

Note that the weight for these speed-flow tests should be the same weight as for method X, your test for VLD. However, for correcting any differences, the model provides a conversion feature.

Method C
Find minimum sink (VMS) or best L/D (VLD) sink rate with the engine off: You can find the speed for VMS directly with your vertical speed indicator (VSI) or GPS, or you can first determine your best glide (VLD) speed with your GPS as above. If you use the GPS, multiply the VLD speed by 0.76 to get the speed for VMS. Once you have the speed(s), you can fly at that speed and measure the sink rate. Of course, either of these requires you to turn off the engine! If you don’t want to do that, see methods B or C. With this method you can directly enter the sink rate on the spreadsheet, but it will be a higher sink rate than the other methods and by an unknown amount.

It’s been explained to me that there are accuracy issues involved with using a VSI because of temperature. Best accuracy will be had with either an altimeter and stopwatch or with the GPS vertical speed field.

4. BUILDING AND USING THE MODEL

  • Knowing that induced  and parasite  drag have fixed relationships at three points—VMS, VLD, and Carson’s —I was able to build a spreadsheet that illustrates the model.
  • The spreadsheet works well for the RV-6A, RV-7A, C-150, 152 and 172 (1959 and 1978). Try it on your aircraft. Let me know your findings. My e-mail address is at the top of this page .
  • Use one or more of the methods. More is better. Method A is the best. I found using methods A and B allowed a good cross-check on the data and more: between them they measure propulsive efficiency.
  • The math built into the spreadsheet will tell you your VMS, your L/D, your horsepower (THP and BHP) at a given speed (assuming a propulsive efficiency), and even your fuel flow assuming a BSFC. The BHP and fuel flow calculations require additional assumptions. As shown in the methods, you can also work from fuel flow (with assumptions).
  • If you already know or think you know the VLD and the glide ratio, you can use the model to check the results to verify your numbers. You can work from VLD or cruise speeds iteratively or with the “Start Here & Method A” page.
  • The spreadsheet illustrates (Douglas Adams’) Dirk Gently’ s premise: the “interconnectedness of all things.” If one thing changes, many things change. The model shows this in ways that may surprise you.

5. IN PRACTICE
Start with accurate instruments! I flew my RV-7A at several speeds including very slowly and used the calibration function on my GRT EFIS/AHRS (Grand Rapids Technologies electronic flight instrument system/attitude and heading reference system) to correct the TAS using GPS. The GRT tells the amount of correction. I used that correction manually to convert IAS to CAS. It’s not perfect, but it’s pretty good. I validated the TAS/CAS correction using the National Test Pilot School three-leg method because GRT uses a two-way method. Instruments needed for this method: a comparable EFIS, a Garmin 196~496, and optionally a precise AOA. I used a lift reserve indicator (LRI). You should also have an E-6B flight computer, but the spreadsheet provides a page for converting TAS to CAS given density altitude. For some methods you will also want a good fuel flow instrument and all-cylinder EGT. VSI readings are subject to temperature error, so I think using GPS for sink rates is best. Last and not least, for DA you will need a good OAT gauge. See Paul Lipps’ article   in this same issue of Experimenter.

I have not tried it, but you may be able to substitute very accurate tachometer readings for fuel flow and your well-tuned ear for best power settings instead of EGT (requires fixed-pitch prop). Power varies with rpm difference squared, all other factors being held constant.

LRI
The LRI is an inexpensive and accurate way to determine AOA.

GRT
Grand Rapids Technologies has been a key digital engine information system player for years,
and it’s now marketing the full gambit with its EFIS/AHRS.

EIS
The Grand Rapids Technologies EIS (engine information system) has been a staple for experimental aviation since 1991.

Make Test Flights - I made repeated flights at various (low) altitudes to determine my minimum power speed for level flight minimum sink: VMS. Kevin Horton is correct that this is touchy. It’s pretty easy to fall off the right number into the back of the power curve. My digital (increment of 10) tachometer was the best indicator for least power. Since my prop has fixed pitch, I simply tried to vary the rpm by 10 up and down and waited to see if it would hold. It’s easier to work down to the VMS point because once you are below it, a lot more power is needed immediately. The good news is that my results were always the same after some very small tweaks. My CAS for VMS is 73 knots, probably plus or minus no more than ¾ of a knot. I’m not that good a test pilot; you will likely do as well or better. As noted below, I also did test flights with a GPS to find the CAS for best L/D VLD. Of the two techniques I think the GPS is better. The results agreed. Now I knew where my curve fell on the x-axis.

I used methods A and B to test the model in the real world. In practice I found that steady readings are easier to get with Method B, but it needs assumptions about BSFC and propulsive efficiency. Method A is theoretically superior. I was able to compare them. With only a few tests, the methods agree pretty well. I had to adjust the numbers for my Catto prop’s efficiency to 85 percent, which is the high end of normal (I had been using 82 percent) to get the readings of fuel flow to match predictions. I compared them on their resulting calculated sink rate at VLD CAS mph. For Method A it was 833 fpm, and for Method B it hovered around 833, within about 2 percent. Of the two assumptions, propulsive efficiency is the least knowable in advance, so that is what I adjusted. Adjusting BSFC did not produce the right results to match reality and is more empirical when LOP.

hile both propulsive efficiency and BSFC can only be estimated, a BSFC of 0.40 (LOP) is based on a large amount of research on this kind of engine (Lycoming and clone), and the values for a good fixed-pitch prop are generally taken to be 80 percent to 85 percent. The comparison of the two methods is thus an excellent way to refine the estimate for the propulsive efficiency.

Evaluate Results - While there is room for doubt about the precision of the measurement of VMS this way, I see no reason to think it’s any less accurate than the iterative method of finding best L/D VLD speed. The problem is in the flying, not the theory. It turned out to be very accurate—see GPS method below. The tests of Methods A and B were reasonably consistent and match reality quite well. The result for calculated drag at VLD is very consistent with CAFE data for the RV-6A. The results are also consistent with verified speeds and fuel flows. The model works!

6. ADDITIONAL DISCOVERIES
Pitch and Power - I believe that I have discovered perhaps an end to the timeless debate over what controls airspeed and what controls altitude. I’m now a firm believer that power controls altitude or sink, and pitch (actually angle of attack) controls airspeed. I experimented with partial-power glides to find the angle of attack at which minimum sink would be. It soon became obvious that the IAS for a given angle of attack was the same even for different power settings, while the sink rate would, of course, vary inversely with power. This was at equal weights and in equal air conditions; we know that a single AOA will produce different airspeeds if weight is different. Using the same AOA (and thus the same airspeed) with various power settings, I found that minimum sink was always at the same AOA and speed (under conditions of equal weight and equal air) even though the rate of sink would differ with power. The same was true for best glide ratio.

AOA Interpretation - I note in passing that this means that my AOA instrument, the LRI, which is a pure pressure gauge and has no electrics, is a valid and reasonably accurate backup airspeed indicator for all speeds in its range, which is those speeds below VLD. I also think, contrary to some, that the LRI is an AOA and nothing more.

A GPS Alternative - I also discovered that my Garmin 496 and 196 can be used to find VLD as described in the methods section. The model predicted 96 knots for my RV-7A’s best glide, and that’s exactly what the CAS was for best glide, when tested this way.

More Testing - I made other flight tests with idle power at 75 knots IAS (73 CAS) and observed sink rate is around 800 fpm. This method proved much more stable and thus more easily observed using the digital readout on the GRT. This was consistent with similar tests made last summer. The engine-out sink rate at this speed turned out to be much more. I chickened out and did not complete my engine-out measurements. Is it prop drag, or is there residual thrust? Both? The model can help answer that by applying the methods.

7. FINDINGS AND CONCLUSIONS
Final evaluation and reality check: The observed 73 knots CAS is within the range for the CAFE RV-6A with a VLD of 106 mph (4 percent possible error = 101.8 ~ 110.2), which computes to 67-73 knots VMS. Since induced drag for a given airframe is mostly the result of the weight, and that is 75 percent of the total drag at VMS, we’d expect two aircraft with the same airfoil such as the RV-6A and the RV-7A at similar weights to have very similar VMS, even with differences in parasite drag from different wingspans and gear legs. CAFE says 106 mph for the RV-6A, and my RV-7A best glide is 110 mph at a slightly lighter weight. If the measurements are equally accurate, my airplane should have more drag than the RV-6A. However, my best estimates are that my minimum drag in pounds is roughly equal to the RV-6A’s while at a slightly higher speed. The numbers are very close. Reality check passed.

The primary findings are that the model is both theoretically sound and usable in the real world without exotic instruments. It works; it’s reasonably accurate and the resources are common.

A secondary finding is that the model reveals weaknesses in test data even for the best testers such as CAFE.

8. CAFE MEASUREMENTS
CAFE has broken important ground and begun the needed accurate testing of homebuilts. It deserves our praise and gratitude.

Over time, CAFE has used different methods for different airplanes, but it can happen that they are occasionally mathematically wrong, and sometimes their numbers are internally in conflict. For example, its THP calculations for the RV-6A were in error (this was recently confirmed in correspondence). To err is human; CAFE is by far the best we have, but it is worth noting it is not perfect.

Further, it reports speeds at VMS and at VLD in many cases where the relationships don’t conform to the requirements of the drag polar model. Something is therefore amiss. For example, for the RV-6A, if the minimum sink rate is 749 feet/minute and the speed for that is either 80.5 as reported or 4 percent more, 83.8, then the drag at VLD is at least 145 and as much as 151 pounds as opposed to the 134 pounds reported. At a minimum, either the sink rate is wrong or the drag is wrong; they cannot both be correct. 134 plus 4 percent is only 139.

CAFE Reports:

 

Glide Ratio

Best L/D mph

Best Glide Sink Rate

Minimum Sink Rate

Best Glide to Minimum Sink Ratio

RV-6A

11.39

106

816

749

1.089453

RV-9A

12

95

694

664

1.045181

RV-8A

9.5

106.8

984

908

1.0837

T-18

10.6

112.7

931

820

1.135366

Lancair Legacy

13.3

158

1042

1038

1.003854

GlaStar

10.6

86.856

717.88

661

1.086051

For RV-6A, Glide Sink computed from CAFE Glide Ratio

The model proves that in every case, the glide-sink-to-minimum-sink ratio should be 1.14. Also, the glide ratio for the RV-8A is not reasonable when compared to the RV-6A, RV-9A, and Thorp T-18. The RV-8A has essentially the same wings as the RV-7A, which performs the same as the RV-6A, and the frontal area of the RV-8A fuselage is smaller. An RV-8A should glide a little better than an RV-6A.

CAFE Zero Thrust Method
CAFE developed and used a method of detecting the exact throttle setting, in a glide, at which there was zero thrust. It uses the slight fore-aft movement of the prop in its shaft bearing for this. It is an excellent way to make testing uniform, but it takes the prop out of the measurement, while in real life a stopped prop will provide some drag. When compared to the methods I propose, the CAFE method should give a result that is closest to my methods A and B (I think). CAFE did not use the zero thrust method in all cases, so its measurements are to that degree less comparable between aircraft; different methods give different results. That said, the zero thrust method is safer! My Method C needs a stopped prop at either VMS or VLD to find the sink rate. The zero thrust method should get you closest to being able to predict drag and thus fuel flow at various flight speeds. My methods A and B are logically the same as CAFE’s zero thrust.

9. NEXT STEPS

  • I want to correct any errors my readers will point out.
  • The flight-testing needs to be done with more trials using the various methods and then their results compared.
  • I want to flight test a C-152 to prove that VMS in level flight is equal to VMS using the CAFE ZT technique. My first try at this was within 5% of ZT results.
  • I want to use Method A, both versions, at a series of altitudes to prove or disprove the problem seen in the Cessna data really is from the propulsive efficiency.
  • I want to offer more examples of the model applied to both experimentals and type-certificated aircraft. Reader contributions are therefore solicited! Send in your data please!
  • I want to find a better way to use propulsive efficiency because it should not be a constant, and in this model it has no empirical basis, only deductive. The methods offer some approaches for this.

 10. DETAILED PREMISES AND DEDUCTIONS

  • If test results do not conform to the model described here, then at least one measurement is in need of correction. That’s essential.
  • The drag polar is always the same mathematical shape. This and the following statements are always true for all fixed-wing subsonic aircraft (or at least in the performance range of most experimentals).
  • That shape is the result when induced drag declines as the square of the CAS and parasite drag increases as the square of the CAS.

Drag

  • The CAS for best L/D (VLD) equals the CAS for minimum sink (VMS) times 1.316.  VLD = (VMS x 1.316).
  • The drag quantities for induced and parasite drags are always equal at VLD.
  • At VMS, the parasite drag is always 25 percent of total drag, and induced is 75 percent. At Carson’s speed, these are exactly reversed. See spreadsheet.
  • Total drag can be calculated from weight and sink rate at any given TAS with power off.
  • THP is total drag times TAS (not CAS) and is the same as power required for a given CAS that equals that TAS at a given moment in level flight; that power curve can be graphed on the drag polar.
  • We can compute that VLD requires 14 percent more THP than VMS.
  • CAS for VMS can be observed by finding the speed at which the least THP is required to maintain level flight. It’s the best endurance speed. From that, CAS for VLD can be computed (x 1.316) and THP for VLD (x 1.14) as well. THP requires correcting the IAS to CAS to TAS, of course.
  • In a gliding airplane (weight times sink rate) equals (drag times TAS). Since (drag times TAS) also equals THP, (weight times sink rate) equals THP. Thus for a given aircraft at a given time with no weight change, the difference in sink rates for two airspeeds is proportional to the THP differences for those speeds. From this we know that the sink rate at VMS times 1.14 equals the sink rate at VLD.
  • Best L/D is what it says—the lift (equals weight) divided by the drag. It is VLD.
  • The glide ratio of the aircraft can be determined from L/D geometrically. It’s almost the same at ratios near 1-to-10. L/D can be computed from just the weight, CAS at VLD, and sink rate at VLD.
  • The glide ratio of an aircraft, expressed in the form 1-to-10, for example, when combined with a stated gliding speed for that ratio can be used to compute the sink rate by a2 + b2 = c2. When a glide angle is stated it can be converted to a glide ratio using simple trigonometry. When the angle and the ratio are stated they should agree. Conversely, if we know the glide ratio and speed we can compute the sink rate.

* The author can supply other spreadsheet formats on request.

Osh365

 
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