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Low RPM, Slow RV-6

Mark7986

Member
Some details: New rv owner, 0-320 150HP, 78 degree pitch prop, internal timing of engine OK, carb heat box works properly, getting full though on throttle,compressions are good, 2100 rpm static, 2450 rpm flat out at 8000 feet 145kts, prop does not unload very fast - takes a long time to get to 2450, 9.3 gph @ 75% power, ball is one ball width to right at cruise, wheel pants and gear fairings installed. Suggestions will be very welcome.

Mark Craven
Fairmont, MN
 
Overpitched

Hi Mark,
Our prop is only 76" pitch on our 180 HP 6A and that's a lot of pitch, intended for max cruise speed and we do 175+ TAS at 7500 and it turning 2700 RPMs.

Your prop seems overpitched by comparison with ours. Can you borrow a flatter pitched prop? It doesn't seem like you're leaning the engine enough if you're burning 9.3 GPH in an 0-320. We burn 9.5 at 7500'/2700 RPM, leaned.
Regards,
 
You don't say what kind of prop. If it is wood, then pitch cannot be compared other than to another prop of the same manufacturer and same diameter. If you are cruising with the ball that far off, you need to address trim problems first.
 
pierre smith said:
Hi Mark,
Our prop is only 76" pitch on our 180 HP 6A and that's a lot of pitch, intended for max cruise speed and we do 175+ TAS at 7500 and it turning 2700 RPMs.

Your prop seems overpitched by comparison with ours. Can you borrow a flatter pitched prop? It doesn't seem like you're leaning the engine enough if you're burning 9.3 GPH in an 0-320. We burn 9.5 at 7500'/2700 RPM, leaned.
Regards,

Pierre, double check the 76". Your numbers would make sense for 86"....

Mark,

I've collected a few 'samples' of RVs with the FP Sensenich and have a rough rule of thumb for their performance. I believe your TAS sounds about right. What you may need to look into is your description of the motor 'labouring' to get to 2450 RPM.
 
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Leonard_Smith_nz said:
Pierre, double check the 76". Your numbers would make sense for 86"

No, he's right on. I've got a 76" Catto on my 180/ RV-6 and I'm pretty close to those numbers. As Mel suggested, a 76" Catto and a 76" Sensenich are two very different things.

78" is the recommended pitch for a Sensenich for a 150HP RV-6. Have you checked the accuracy of your tach?
 
sprucemoose said:
No, he's right on. I've got a 76" Catto on my 180/ RV-6 and I'm pretty close to those numbers. As Mel suggested, a 76" Catto and a 76" Sensenich are two very different things.

78" is the recommended pitch for a Sensenich for a 150HP RV-6. Have you checked the accuracy of your tach?

Jeff,

My mistake...assumed both were talking about FP Sensenich.
 
Before I took the 320/FP sensenich off of my latest RV6 I had numbers a little higher than that (and yes, mine was a 150)...

My engine was brand new (built by me), and my Sensenich was 79". I could pretty easily pull it up close to redline (2600 on that prop). I REALLY would NOT consider going all the way down to 76" on a 320. That redline is a hard number. Better to be just under than poking around 26.

Like others have said, pitch numbers on wood props are useless when compared to the metal ones, and even useless when compared to other mfgrs of wood props. Totally depends on the airfoil, blade length, etc......

I'd be more inclined to check a few other things before repitching the prop. Typically these metal sensenich's yield around 150RPM / Inch, so losing 2 inches in pitch from your 78 to 76 would probably give you well over the redline....NOT a good thing on that prop!

I'd check the airplane, tach, asi, rigging, etc...get a good GPS, calculator and do a bunch of runs to really ensure your numbers are accurate.

Anyway, don't know what else to tell you except that 78" should be perfect on that engine.....

Cheers,
Stein.

RV6's, Minneapolis

P.S., for an apples comparision the 180 on our other -6 has an 85" sensenich prop on it, and I can pretty easily wind the engine up to 2850RPM..........but the engine is good & strong, and the plane is clean & light!
 
Timing....NOT MAGS... read on..

There is an all too common cause (read stupid mechanics) of low power output. In the following described instance, you will get close to rated static RPM, but low climb rates and slow cruise.
The cause here, and this is an extreme analysis, but I have seen it in several planes (one that made it to TBO actually, with sucky power) is , believe it or not.....
.
.THE CAMSHAFT/CRANKSHAFT TIMING IS OFF ONE TOOTH!!!!!!!
.
. Yes ladies and gentlemen, this happens, continues to happen and your engine will run and start just fine with this condition. Performance, well that is another story. First my personal history with this, then how to easily see if you are a suffering from this problem.
In my Kitfox, when I built it, in my LYC IO-290, I paid a "reputable" engine builder based out of Lantana airport in Lantana Fl. to put together the bottom end, and he did just that to me.(among many other really bad things, don't get me started)...(PM me for the name of this, umm "mechanic", if you already don't know who it is. STAY AWAY!!!) My flying symptoms were....700 instead of 1100 fpm.....Normal static RPM as expected....Cruise was 122 instead of the expected 135...I tried several props, same thing....
.

Now, easy analysis of this anamoly.....Pull a valve cover off of any cylinder....Pull out spark plug and put piston to TDC of the of exhaust stroke(Look into SP hole to hit TDC, or use timing wheel,..whatever...)..... Rock piston back and forth at TDC.Now, note the exhaust valve and intake valve ( actually note the rockers...) at exactly TDC in this position, the ex. valve should close and the intake should open. ....I am not sure if hydrolic lifters will be exactly like solid lifters at this point....Anybody add here???? Rocking the piston back and forth, with the prop in your hand, will show if you are timed correctly...
I certainly hope this is not it, or the engine will soon be coming off to fix...Just another idea for head scratching/hangar flying....
.
Bottom line here, your climb performance will obviously be more degraded than cruise, since it takes a whole lot of HP to get a little more MPH.
.
.PS, one mechanic said in his humble observation, this happens in at least one out out of 1000 rebuilds. He said he even heard of an engine coming factory new from LYC. in this condition......Also, how much power you lose, depends on whether you are advanced or retarded one tooth........
Glen
 
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Thrust - Drag = Speed

A quikcalc shows that turning 2700 rpm (new prop) you should go 175 mph. That is still about 10 mph slower than spec. The previous post are all interesting, good and possible.

Going to the equations again, speed is a function of drag and thrust. Work on both. The previous post talk to prop and engine issues, which is excellent, but what about the drag part. I understand you have the fairings on.

Do you have any pictures of your plane? Put it out in the middle of a flat ramp, support the tail, for a level flight, naturalize position of all controls (temporarily with tape if needed). Now walk around, a little ways back, get down and get a good look at it with a critical eye. Sometimes you measure stuff within a nats hair in the hanger but out on the ramp you can see that right wheel fairing is a little a skew inboard at the trailing edge. When you fly is your elevator in trail or in other words the elevator counter balanced arm even with the Horz stab in flight? Ailerons even in flight?

Than get up close top to bottom and look for any place air is getting hunk up. Are the engine baffles sealing well. Cooling drag is a big part of the total drag. In a word are all the fairings on straight. Are the controls all in a fair-ed and rigged (even left left to right). Are there any gaps and uneven surfaces.

My guess is a little from here (thrust) and a little form there (drag reduction) you will approach the book speed of about 185 mph 75%, 8000" cruise. I had a similar experience with my RV from the time I first flew it and from the time I had tweaked it over a year or two, gaining at least 10 to 15 mph. Sorry non specifics but a bunch of little things. Recommend back articles by Van in the RVator ('92 thru '94 especially) about increasing speed and the book, Speed w/ Economy by Kent Paser. It's a mph here and mph there.

The last comment and have no idea, but possible measurement error is always a possibility? It happens to everyone. The methods are much easier today and assume you used GPS, with three constant course/track runs and used Kevin Horton's spread sheet to crunch the numbers. As far as power estimate you should have both RPM and MAP. The FF is good info, and your sound a little high for 75% power on a 150 hp engine?? Many guys with out FP don't put a MAP gauge in. That is a small pet peeve. You really need a MAP gauge in an experimental plane.

Bottom line you need more thrust and less drag. Think and attack everything that would reduce power / thrust and increase drag. The only thing obvious is the low RPM, which can be a prop, engine or both. Remember this is the fun part, hunting down that extra speed. :D :rolleyes:
 
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glenmthompson said:
There is an all too common cause (read stupid mechanics) of low power output. In the following described instance, you will get close to rated static RPM, but low climb rates and slow cruise.
The cause here, and this is an extreme analysis, but I have seen it in several planes (one that made it to TBO actually, with sucky power) is , believe it or not.....
.
.THE MAG/CRANKSHAFT TIMING IS OFF ONE TOOTH!!!!!!!
.
. Yes ladies and gentlemen, this happens, continues to happen and your engine will run and start just fine with this condition. Performance, well that is another story. First my personal history with this, then how to easily see if you are a suffering from this problem.
In my Kitfox, when I built it, in my LYC IO-290, I paid a "reputable" engine builder based out of Lantana airport in Lantana Fl. to put together the bottom end, and he did just that to me.(among many other really bad things, don't get me started) My flying symptoms were....700 instead of 1100 fpm.....Normal static RPM as expected....Cruise was 122 instead of the expected 135...I tried several props, same thing....
Now, easy analysis of this anamoly.....Pull a valve cover off of any cylinder....Pull out spark plug and put piston to 180 deg out of TDC from comp. stroke, as in top of exhaust stroke(Look into SP hole to hit TDC, or use timing wheel,..whatever...)..... Rock piston back and forth at TDC.Now, note the exhaust valve and intake valve ( actually note the rockers...) at exactly TDC in this position, the ex. valve should close and the intake should open. Rocking the piston back and forth, with the prop in your hand, will show if you are timed correctly...
I certainly hope this is not it, or the engine will soon be coming off to fix...Just another idea for head scratching/hangar flying.
Glen
I'm not quite clear on what you mean by one tooth. The mags are adjustable throughout a certain range by simply loosening them and rotating. If they are off by more than that, they are considered one tooth out, and have to be removed, and the drive gear moved one tooth over. A simple mag timing test would reveal this however, no need to pull a rocker cover off.
 
Hi Mr. Ox Man!!!

Lemme explain a little further...the timing I am refering to, is how the crankshaft gear in the back, inside the accessory case, is meshed with the gear on the back of the camshaft. This is known as "valve timing"..NOT ignition timing. Sorry, I corrected my above post, I DID say mag instead of camshaft, thus how I confused you...sorry, my bad....
As far as the mag timing, yep you are correct, but I speak of the "other" gear meshed with the crank.
...Hard to believe that somebody who works on SEL planes would do this, but....ya never know!
Glen
 
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glenmthompson said:
Lemme explain a little further...the timing I am refering to, is how the crankshaft gear in the back, inside the accessory case, is meshed with the gear on the back of the camshaft. This is known as "valve timing"..NOT ignition timing. Sorry, I corrected my above post, I DID say mag instead of camshaft, thus how I confused you...sorry, my bad....
As far as the mag timing, yep you are correct, but I speak of the "other" gear meshed with the crank.
...Hard to believe that somebody who works on SEL planes would do this, but....ya never know!
Glen
Glen,

It all makes sense now. Yep that could do it, although it'd be an outside shot.
 
glenmthompson said:
There is an all too common cause (read stupid mechanics) of low power output. In the following described instance, you will get close to rated static RPM, but low climb rates and slow cruise.
The cause here, and this is an extreme analysis, but I have seen it in several planes (one that made it to TBO actually, with sucky power) is , believe it or not.....
.
.THE CAMSHAFT/CRANKSHAFT TIMING IS OFF ONE TOOTH!!!!!!!
.
. Yes ladies and gentlemen, this happens, continues to happen and your engine will run and start just fine with this condition. Performance, well that is another story. First my personal history with this, then how to easily see if you are a suffering from this problem.
In my Kitfox, when I built it, in my LYC IO-290, I paid a "reputable" engine builder based out of Lantana airport in Lantana Fl. to put together the bottom end, and he did just that to me.(among many other really bad things, don't get me started)...(PM me for the name of this, umm "mechanic", if you already don't know who it is. STAY AWAY!!!) My flying symptoms were....700 instead of 1100 fpm.....Normal static RPM as expected....Cruise was 122 instead of the expected 135...I tried several props, same thing....
.

Now, easy analysis of this anamoly.....Pull a valve cover off of any cylinder....Pull out spark plug and put piston to TDC of the of exhaust stroke(Look into SP hole to hit TDC, or use timing wheel,..whatever...)..... Rock piston back and forth at TDC.Now, note the exhaust valve and intake valve ( actually note the rockers...) at exactly TDC in this position, the ex. valve should close and the intake should open. ....I am not sure if hydrolic lifters will be exactly like solid lifters at this point....Anybody add here???? Rocking the piston back and forth, with the prop in your hand, will show if you are timed correctly...
I certainly hope this is not it, or the engine will soon be coming off to fix...Just another idea for head scratching/hangar flying....
.
Bottom line here, your climb performance will obviously be more degraded than cruise, since it takes a whole lot of HP to get a little more MPH.
.
.PS, one mechanic said in his humble observation, this happens in at least one out out of 1000 rebuilds. He said he even heard of an engine coming factory new from LYC. in this condition......Also, how much power you lose, depends on whether you are advanced or retarded one tooth........
Glen
The crankshaft timing was one of the things Sensenich recommeded to check, it was right on

Mark
 
I just found this thread and since I have a similar problem I am posting my problem here.

I have 30 hours on my RV-9A with new O320-D2A engine from Aero Sport Power and a 79 pitch Sensenich metal propeller. I don't have my wheelpants neither leg fairing on yet. I have not received my manifold transducer, thus only rpm is recorded. I verified my TAS using Kevin Horton's spread sheet. Following are my numbers:

at 8,500 ft (leaned ROP)

rpm TAS (kts) gph
2080 117 5.3
2190 121 7.7
2290 132 8.4
2420 139 10.0

at 3,000 ft (not leaned)

rpm TAS gph
2080 114 8.0
2290 130 10.1

Yesterday at 6,000 ft, full throttle, I had 144 kts at 2,450 rpm.
At cruise the ball is slightly on the left and the elevator slightly pointing down (I could see an inch of counter-balance/tip above the HS). People on the ground also report a whistling sound from my airplane. During the climb out my #3 CHT could go as high as 450 degree F. At cruise, it is around 390. #1 and #2 are around 310-330. My GRT EIS 4000 reports a carb temperature of 127 degree F. But, I don't see any leaks in my airbox. This might be a sensor/installation problem. I set my idle to 500 rpm per recommendation of Mike Seager and adjusted idle mixture accordingly. Magneto timing has been checked and both side are set at 25 degrees.

Apparently I have problems with my low rpm at full power and the higher than normal fuel flow. I am a newbie to engines and still learning.

I will look into suggestions already given on this thread. Any additional suggestions will be appreciated.

Ted
 
Ted,

I think your aircraft's performance is within reason for an RV-9 without fairings or wheelpants. The fuel burn numbers look high, but that could be a product of several different issues - tach accuracy, rich mixture, etc.
 
For the original

In a fixed pitch prop situation, with a common design airplane with known performance characteristics, well built and rigged, at a set RPM with an accutate tach how can it be anything but a bad prop?

Bob Axsom
 
Vans told me it takes 22-28 HP withour gear leg and wheel fairing. My counter weights are also slightly above the stabilizer.

Mark
 
Close but no cigar

Bob Axsom said:
In a fixed pitch prop situation, with a common design airplane with known performance characteristics, well built and rigged, at a set RPM with an accurate tach how can it be anything but a bad prop?

Bob Axsom
Dear Bob, the prop has to work with the airframe and engine, they are all interrelated. It may not be a prop issue but an engine or even airframe issue. Not all airframes and engines are the same. I understand your point, most RV's get pretty consistent performance from one plane to another. However you, "Mr. Speedy" :D, should know with all the work you have done on your bird, that small seemingly unnoticeable changes (unnoticeable to an outside uninitiated observer) can make a big difference. There are ways to milk speed out of any stock RV. If he reduces drag he will increase speed and of course RPM, with out a prop change. I'm going to keep my speed secrets, secret for now, since I might be racing you some day. :D
 
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Well Shucks, I thought I had it

Sure sounds like an over pitched prop at arms length but I'm sure that several things could be improved to get more speed in the lift/weight/thrust/drag trade-off. Flying in cruise with down elevator in Mark's latest post got my attention. That could be rigging, CG or thrust line related.

George, I know from previous posts you raced before and it would be great to have you in the Air Venture Cup Race in the future. It is pure racing with no gimicks and both the quantity and quality of people and airplanes are very good. 407 nautical miles at wide open throttle and high RPM and the short recovery leg up to Fond Du Lac requires some fuel planning but it's a good race.

Bob Axsom
 
Thanks Bob, you probably are right

Bob Axsom said:
Sure sounds like an over pitched prop at arms length but I'm sure that several things could be improved to get more speed in the lift/weight/thrust/drag trade-off. Flying in cruise with down elevator in Mark's latest post got my attention. That could be rigging, CG or thrust line related.

George, I know from previous posts you raced before and it would be great to have you in the Air Venture Cup Race in the future. It is pure racing with no gimicks and both the quantity and quality of people and airplanes are very good. 407 nautical miles at wide open throttle and high RPM and the short recovery leg up to Fond Du Lac requires some fuel planning but it's a good race.

Bob Axsom
Hey Bob you are right, it sure sounds like over pitched prop, but there is something else going on. At least that is what I think. A little of this and little of that, but probably mostly the prop?

Thanks for the invite, love to join you at the race. I am working on it. When I make the show I will be sure to say hi.

BTW I just saw this on jamesaircraft Yahoo group. Another gent did some lower baffle work that was very interesting. Check it out in the photo section. I'll try to link below:

a051.jpg

8454.jpg

7b6b.jpg

e83c.jpg

46d7.jpg
 
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gmcjetpilot said:
Hey Bob you are right, it sure sounds like over pitched prop, but there is something else going on. At least that is what I think. A little of this and little of that, but probably mostly the prop?
But, apparently he has the pitch that is recommended by Sensenich (78"), and Stein said that on his 150 hp O-320 powered aircraft, that it would turn up to almost 2600 rpm.

So, it must be either an engine that isn't making the expected power, or an airframe with much, much more drag than normal, or a bad tach, or bad airspeed info, or a prop that isn't at the pitch that is advertised (i.e. the actual pitch does not match the part number).

Mark - you say you get 145 kt at 8,000 ft. Is that IAS or TAS? If it is TAS, please detail how you determined the TAS.

You checked the tach, and reported it was good. Just to be sure, check it again, using yet another prop tach. Do the check at several rpms. I'm not an expert on prop tachs, but is it possible to use one in flight? If not, given that you can only get 2100 rpm statically, you aren't able to check the tach at the rpm of interest (2450 indicated rpm). You might have a tach that reads correctly at lower rpm, but reads too at higher rpm. Try to borrow a different tach.

It would be awfully strange if the prop pitch didn't match the part number, but stranger things have happened. Find another RVer with a 78" pitch Sensenich. Get a digital level, or some other similar reference. Turn the props so they are horizontal. Use the digital level to measure the pitch at the end of both ends of each prop. The aircraft pitch attitudes will probably differ, so for each prop, average the angles you measure on the two ends of that prop to remove the effect of the pitch attitude (you'll need to get creative on the math here). Repeat these comparative measurements at a few other stations measured in from the prop blade tips.

Assuming this is a power problem - confirm you are getting full throttle. Confirm no intake obstructions. Do one flight without the air filter installed. Do a compression check.

Good luck. Keep us posted.
 
Here the update. I got looking at the airframe over the weekend and noticed the fairing between the gear leg fairing and the fuselage was hanging down. I pushed them up tight to the fuselage and taped them there. Test flight at 8000 feet, 23.5 MP, 2450RPM--true A/S was 158Kts. using garmin 430 to calulate the speed. Thats 13 knots increased. Today I had an appointment at the prop shop. They found the prop was much closer to 79" then 78". they repitched to to 77". Also on one blade on one section was more then 1 degree off. During the static balance it was determined it was way off. They had to grind one side down to balance the prop. The trip home 2000 feet full throttle airspeed went into the yellow. At 8000 still got 160 knots true. I think the takeoff and climb was improved, however the prop still didn't unload very fast. We're gotting closer. Thanks for all the help. Next on my list is the elevator.

Mark
 
Now you are in the right ball park

Now you are in the right ball park Mark. My guess is you should be able to get between 165 and 170 kts if everything is right but 160 is probably as good as most owners are getting with an O-320.

Bob Axsom
 
Van's perf data shows 187 mph TAS at 8000 ft for a 150 hp RV-6. 160 kt TAS = 184 mph TAS. You are starting to get into the range of normal aircraft to aircraft variation of performance.

You say you are using the GNS 430 to calculate the speed. I'm not sure what that means. Does the 430 have a function where you can input IAS, altitude and temperature and it tells you the TAS? If so, there may be errors in your indicated airspeed. Most airspeed systems have some error, and this could easily be 5 kt or more.

Or, are you taking the GNS 430 ground speed and somehow manipulating it to get TAS. You can't simply take average ground speed over various headings to get TAS. This will only provide an accurate TAS if there is zero wind. If there is wind, the amount of error is small if the wind is low, but the error may be quite large if the wind is strong.
 
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Congrats Mark; Agreed Kevin

Kevin Horton said:
But, apparently he has the pitch that is recommended by Sensenich (78"), and Stein said that on his 150 hp O-320 powered aircraft, that it would turn up to almost 2600 rpm.

So, it must be either an engine that isn't making the expected power, or an airframe with much, much more drag than normal, or a bad tach, or bad airspeed info, or a prop that isn't at the pitch that is advertised (i.e. the actual pitch does not match the part number).Good luck. Keep us posted.
I totally agree, that was my original point of my post to Bob. I was just stating on first it does seem the prop is off pitch a little. However I think it could be a little of everything, engine power, drag. My first post was

Thrust - drag = speed. Maximize thrust, minimize drag.

Again I agree with you 100%. It still could be a little bit of the prop?

Did any one check to make sure it is pitched properly? Doha! It may be off?


PS: Hey Mark good on you for finding the fairing and checking the prop. Make sure all your other fairings are tight and not opening up in flight, gapping or shifting. Give that engine a good tune up: Clean the air filter, clean and gap the plugs (bomb test them), change the oil and filter, check the timing and compression of not done yet. If still down on power how old are the points? Sounds like you had real speed brakes with those saggy gear intersection fairings.
 
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Shim in design

When I built my RV-6A there was a shim I had to make out of some fairly thick aluminum as I recall and it went under the forward part of the horizontal stabilizer. If that isn't in there it could be forcing you to compensate with down elevator in cruise. Another thing to recheckis the wing incidence angle. The method specified seems a little crude but it works fine - level the canopy deck (x and Y plane) stand the specified block over the rear spar and lay a 48" level on the forward spar location and the block and the bubble should center. If that is off there is a way to fix it without touching the wing but I hesitate to mention it. I will say that the relative fwd and aft angle between the wing and horizontal stabilizer is what provides the pitch stability and I suspect you have an overly stable airplane.

Another thing I did on my gear leg fairings to fuselage interface was to seal the interface and only that (top) interface with silicone RTV. Since one fairing was "hanging down" you may have some big gaps in this area.

Bob Axsom
 
Mark7986 said:
Garmin 430 is an IFR Cert. GPS Capable of Calulating TAS.
But, what data does it use to calculate TAS? It doesn't have pitot and static lines going in the back, so it doesn't know what the IAS is. Do you manually input the IAS, temperature, etc? If so, have you done testing to determine what the error is in your indicated airspeed system? It almost certain has some error. It might only be 1 kt, or it might be 10 kt. If you are using the TAS as a measure of goodness of your engine, prop, airframe, etc, then it is important to know what error the TAS value has.
 
TAS calc or Ground speed based TAS?

Kevin Horton said:
But, what data does it use to calculate TAS? It doesn't have pitot and static lines going in the back, so it doesn't know what the IAS is. Do you manually input the IAS, temperature, etc? If so, have you done testing to determine what the error is in your indicated airspeed system? It almost certain has some error. It might only be 1 kt, or it might be 10 kt. If you are using the TAS as a measure of goodness of your engine, prop, airframe, etc, then it is important to know what error the TAS value has.
Not sure about the 430 Garmin. The Dynon EFIS has TAS if you have the OAT probe attached. However I would not rely on that for flight test data. For cruising around TAS on the Dynon is fine.

To get good TAS, the Temp has to be perfect, Baro setting perfect and IAS, which we know has some error, needs to be corrected (CAS). I get what you are saying Kevin, ground speed average (per your three leg constant course method) is more reliable and accurate. We will never get 0% error, but when you are hunting down 1 or 2 mph the ground based TAS is best.

However I see the other point, in the context of this discussion the speed started off being way off. Good news is he found 13 kt laying around with some tape in fairings. So for gross changes, calculated TAS was good enough to find a big change.
 
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