rv6ejguy

Well Known Member
The DH diesel discussion has me intrigued with what more people are seeing in the real world with their Lycomings running LOP. Perhaps we can work out approximate BSFCs from the drag polars and Van's basic speed data.

Feel free to post your numbers here, fuel flow, TAS, type of RV.:)
 
RV-9A Dual EI/Carb/Hartzell

Hi Ross,

RV-9A dual EI/Carb/Hartzell

LOP at 2 settings:

6.0 GPH 148-150KTAS 6000ft and above

5.0 GPH 128-130KTAS down low

I run at one of these 2 settings 90% of the time.
 
Here's mine..

RV-7, Extreem IO-360 from Eagle Engines.
Silverhawk FI, dual P-mags, 2.blade M/T prop.

22 litres/hr (5,8 US GLS), 130 KTAS, 50* LOP at 5000' and below.

24 litres/hr (6,3 US GLS) 150 KTAS, 50* LOP at 10.000.
 
My Two Cents

1. My real SFC when LOP is about .40 but the GRT tends to exaggerate because it is using RPM and MP for its calculation along with FF and RPM & MP don't produce the same actual power when LOP vs. ROP. The GRT will compute it down to .38 or even .37. Lycomings tend to do a little worse - maybe .41 or .42. Higher compression or electronic ignition tend to improve it. See GAMI articles on this Forum for extensive information on that.

2. Deducing SFC from the drag curves is only possible if you have a correct value for propulsive efficiency, most of which is the efficiency of the prop itself and some of which is losses due to interference between the prop wash and the airplane. You have a better chance of deducing your propulsive efficiency using a fixed value for SFC. For much more on this see my article, link on my website or signature below.
Also, in order to deduce anything from the drag curve you have to know what it really is. For a 6-A you could refer to the CAFE article. Ditto for the 9A. All others must punt. There is an 8 or 8A write-up but the result on drag do not IMHO compare correctly to the others. For most of us, propulsive efficiency will be in the range of 82 to 87 %. Feel free to debate this.
 
6A, 180 FI/EI/CS, 158 to 162 ktas, 7.2 to 7.5 gph, 22"/2300, 7500 to 9500'. Same settings lower, probably lose around 3 to 5 knots. Been cruising with those settings for 1100 hours. It is probably around peak to 50F LOP, depending on conditions. Sometimes I run WOT at 7500', but not often. I set the throttle and rpm to those settings, then adjust for fuel flow. Rarely look at egt's any more (I do the fuel flow vs egt series every year or so to keep an eye on mixture distribution). CHT's are powerful indicator of mixture settings, adjusted for OAT. If I see cht's in the above 350 range with OAT of 70F or so, I dial out the mixture. Lose a few knots speed, but cools things down in to the 330 range right away.
 
If we work back to 135 knots, we're seeing averages of around 4.4gph so far on various RV airframes up in the 6000-10000 ft cruise altitudes. Not bad! My Subaru setup is pretty bad then at about 6.6 leaned to 1400F EGT.:eek:
 
1. My real SFC when LOP is about .40 but the GRT tends to exaggerate because it is using RPM and MP for its calculation along with FF and RPM & MP don't produce the same actual power when LOP vs. ROP. The GRT will compute it down to .38 or even .37. Lycomings tend to do a little worse - maybe .41 or .42. Higher compression or electronic ignition tend to improve it. See GAMI articles on this Forum for extensive information on that.

2. Deducing SFC from the drag curves is only possible if you have a correct value for propulsive efficiency, most of which is the efficiency of the prop itself and some of which is losses due to interference between the prop wash and the airplane. You have a better chance of deducing your propulsive efficiency using a fixed value for SFC. For much more on this see my article, link on my website or signature below.
Also, in order to deduce anything from the drag curve you have to know what it really is. For a 6-A you could refer to the CAFE article. Ditto for the 9A. All others must punt. There is an 8 or 8A write-up but the result on drag do not IMHO compare correctly to the others. For most of us, propulsive efficiency will be in the range of 82 to 87 %. Feel free to debate this.

This would be approximate of course due to variations in prop efficiency vs. speed and rpm plus airframe drag differences. I was more interested in ballparks using Van's or CAFE published data.
 
6A, 180 FI/EI/CS, 158 to 162 ktas, 7.2 to 7.5 gph, 22"/2300, 7500 to 9500'. Same settings lower, probably lose around 3 to 5 knots. Been cruising with those settings for 1100 hours. It is probably around peak to 50F LOP, depending on conditions. Sometimes I run WOT at 7500', but not often. I set the throttle and rpm to those settings, then adjust for fuel flow. Rarely look at egt's any more (I do the fuel flow vs egt series every year or so to keep an eye on mixture distribution). CHT's are powerful indicator of mixture settings, adjusted for OAT. If I see cht's in the above 350 range with OAT of 70F or so, I dial out the mixture. Lose a few knots speed, but cools things down in to the 330 range right away.

Ha! That's funny....because when people ask me what my RV6 cruises at, I often say: "about 7.5 gph". Sometimes that's 160 kts, sometimes less, sometimes more, but in general my numbers are almost spot on with Alex. I too end up cruising around based on fuel flow settings and not so much speed. I usually shoot for 7.5 or 8 gph and whatever that gives me for speed is what it is!

I rarely spend time putting down at the 135 range, but I'll have to do that and see what it ends up like. I know Pete has some pretty good data too with his 9, I'll have to ask a few other 9 guys where they are at while going slow.

My 2 cents as usual,
Stein.
 
Mine Vs CAFE 6A

This would be approximate of course due to variations in prop efficiency vs. speed and rpm plus airframe drag differences. I was more interested in ballparks using Van's or CAFE published data.

My 7A has its speed for best L/D at 96 kts=110.5 mph whereas the CAFE 6A had its best L/D at 106 mph. The 6A had drag at that speed of approx. 134 pounds. My drag at 110.5 is approx. 133 pounds as close as I can estimate it. That is using .40 for SFC and .85 for propulsive efficiency. These are at comparable weights or with mine a little lighter. CAFE's 6A was at 1650#.

I have not completed proving this yet, but I believe that my speed for best L/D is directly comparable to the 6A's, method to method. CAFE used the Zero Thrust technique. I used a number of alternative techniques designed to emulate the result. If you don't get the L/D right then the curve won't be right.

I won't take up the space, here, to show why .40 is the correct result for my airplane, but I believe it is. Kevin Horton thinks it is not that good - we have discussed it - so his data and calculations would say it is .4125 or thereabouts but that would mean my propulsive efficiency would be even higher since my flight data is solid or even conservative. Superior's data says I can do it. GAMI says I can do it. Lycoming not so much. Mine is a Superior XP IO-360+ 180 HP. No matter how you slice it, the individual components (drag curve, SFC, propulsive %) must fit together such that the combination produces the correct flight data (TAS, fuel flow).

My 7A goes 160 kts tas on 8 gph at 8000' with IFR calibrated instruments and the TAS verified with GPS.

I hope this is what you were looking for. If not, come back for more.
 
I won't take up the space, here, to show why .40 is the correct result for my airplane, but I believe it is. Kevin Horton thinks it is not that good - we have discussed it - so his data and calculations would say it is .4125 or thereabouts but that would mean my propulsive efficiency would be even higher since my flight data is solid or even conservative. Superior's data says I can do it. GAMI says I can do it. Lycoming not so much. Mine is a Superior XP IO-360+ 180 HP. No matter how you slice it, the individual components (drag curve, SFC, propulsive %) must fit together such that the combination produces the correct flight data (TAS, fuel flow).

My 7A goes 160 kts tas on 8 gph at 8000' with IFR calibrated instruments and the TAS verified with GPS.

I hope this is what you were looking for. If not, come back for more.

If we assume same prop efficiency and same BSFC then, would you say 4.8 gph would be about right at 135 knots TAS? I worked out the 9A CAFE numbers at 8600 feet DA and it would be 4.1 gph all things remaining equal (which probably don't). This was leaned to peak.
 
Varying It

If we assume same prop efficiency and same BSFC then, would you say 4.8 gph would be about right at 135 knots TAS? I worked out the 9A CAFE numbers at 8600 feet DA and it would be 4.1 gph all things remaining equal (which probably don't). This was leaned to peak.

For my airplane, using 135 kts, 8600 Density Alt. it would be 5.4 gph using the same SFC and prop%. A 9 or 9A should do better. CAFE's results for the 9A were much better than for the 6A. The key to this is the sink rate at best L/D. The 9's long wings make it a better glider.If you look at Van's projections for the 9 versus what CAFE measured, the performance was a lot better than Van claimed.
 
Recent Data Point RV-6A

9500 MSL, 70F OAT, 170 TAS, 7.0 Gal/Hour, about 65F LOP. This in a 185 HP Superior IO-360 RV-6A with dual Pmags.

Hans
 
Hi Ross,

Just so happens I wrote some numbers down day before yesterday.

8500' MSL (DA 10,120') OAT 55F, IAS 128K, TAS 150K (Dynon D10A).
RPM 2480, MP 21.5", FF 7.7 GPH.

LOP after peak, -14, -21, -40, -33.

CHT 357, 315, 316, 339.

That's about all the numbers there are. Hope they make some sense. :)

The engine is 8.5 compression, IO360 running on 2 Slick mags.
 
not looking real flash Ross... ;)

If I use a www.vansaircraft.com polynomial (see the DH thread) on some of the data presented, then:

hevans:

135kts at 8600' and 5.4USgal/h = ~0.48lb/hp.h

160kts at 8600' and 8.0USgal/h = ~0.44lb/hp.h (LOP)

AlexPeterson:

158kts-162kts and 7.2-7.5USgal/h = ~0.388-0.435lb/hp.h (LOP)

(this is a classic example of the need for extreme accuracy on all measurements!)

ao.frog:

150kts at 10000' and 6.3USgal/h =~0.42lb/hp.h (LOP)

Obviously this is assuming a fixed propulsive efficiency (or at least the same as Van's demo/test aircraft)
 
So we are bracketing around 5.3-5.6 gph LOP in a 7/7A at 135 knots. Gotta like Van's designs.:)

I don't feel quite so bad burning 1 gph more with my 6A Sube. The 9/9A would look to be a bit more economical at these speeds than a 6 or 7.

This is all very interesting.

Using Van's speeds and Andy's numbers- well we're in the ballpark of WAM's stated .45 BSFC figures at MC power- what it would need to run at these higher speeds. Should I rest my case?

I was just digging though some data on turbocharged Conti 550s. The factory engines are stated at .406 LOP with 7.5 CR pistons, the 8.5CR normalized versions are stated at .380.
 
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Not in total agreement

If I use a www.vansaircraft.com polynomial (see the DH thread) on some of the data presented, then:

hevans:

135kts at 8600' and 5.4USgal/h = ~0.48lb/hp.h

160kts at 8600' and 8.0USgal/h = ~0.44lb/hp.h (LOP)

AlexPeterson:

158kts-162kts and 7.2-7.5USgal/h = ~0.388-0.435lb/hp.h (LOP)

(this is a classic example of the need for extreme accuracy on all measurements!)

ao.frog:

150kts at 10000' and 6.3USgal/h =~0.42lb/hp.h (LOP)

Obviously this is assuming a fixed propulsive efficiency (or at least the same as Van's demo/test aircraft)
My two data points are using the same SFC (.40) and prop% (85%) so there is a discrepancy between "Van's polynomial" whatever that is and a drag curve based on real data. Please explain the polynomial. Thanks. btw: My 160 kts was at 8000 actual and the projected 135 kts was at 8600'. Link to "DH thread"?
 
Ross,

You may rest your case m'Lud when you've considered the 0.36 claim of Thielert/Centurion and the 0.37-ish of the SMA.

:p
 
Please explain the polynomial. Thanks

I took the Van's published TAS data for 55% and 75% power for each engine power quoted. This gives me six data points to regress a polynomial through which I can then use to estimate the required power for any speed, taking care not to extrapolate it too far!

From the power required, I can work out what BSFC gives me your quoted fuel flow.
 
Ross,

You may rest your case m'Lud when you've considered the 0.36 claim of Thielert/Centurion and the 0.37-ish of the SMA.

:p

Never said these were not slightly better in SFC if you consider 3-5% significant. Life cycle costs on the Thielert buried it with gearbox/ clutch removals every 160 hours and new engines frequently at 250-500 hours not to mention downtime waiting for parts from Europe and then of course what happened next...

SMA, who knows people actually flying them and how they are working with more than 500 hours on them? Have they recovered the $25K+ in acquisition costs yet in fuel savings? I don't hear much but would be interested to know what the real world experience has been with them.

I'm no big Lycoming fan but it is hard to argue with the overall numbers.
 
More discussion

I took the Van's published TAS data for 55% and 75% power for each engine power quoted. This gives me six data points to regress a polynomial through which I can then use to estimate the required power for any speed, taking care not to extrapolate it too far!

From the power required, I can work out what BSFC gives me your quoted fuel flow.

Van is saying that 8000' at max throttle is 75%. It is easily demonstrated that it is significantly more than 75% even though that is a conventional relationship used by Cessna, Piper, etc. Even so, many examples do better than Van's claims. Mine does 201 at 8000' using best power. That's 128.5 THP and 151 BHP according my my calculations. Air density at 8000 is 78.6% of sea level and I get another 1" or more from the ram air effect. My numbers say I'm using 12% more horsepower than Van's is saying.

For a 7A, solo wt, he's saying that you use 135 BHP to go 198 mph and 99 HP to go 177 mph (75% and 55% of 180). My drag curves give me the THP for those speeds - 123.76 and 92.82. The trouble with this is that these numbers give us propulsive efficiency of 91.7% at 75% and 93.76% at 55% power. In this case, propulsive efficiency is THP/BHP. In all cases I correct for Density Altitude where appropriate.

If I plug the CAFE 6A into my model, I get 130.26 THP at 199.7 mph at 7079' and 116.93 THP at 9058' at 191.6 mph. CAFE's results are about the same (there was a small error in the original article). In other words, my model can match CAFE data closely using their L/D and drag numbers. There is nothing fancy about my model. Parasite drag increases as the square of velocity and induced drag declines as the square of the velocity. At best L/D, they are each 50% of total drag. THP is drag times TAS with units corrections.

To get from THP to BHP we need propulsive losses and from BHP to fuel flow we need SFC. I have stared at Van's data for many hours and I don't see any specs for fuel flow per BHP.

I just don't think that propulsive efficiency of 94% is reasonable. Conventional wisdom says props are doing really well to get past 85% and that does not count the loss for prop to airplane interference. Craig Catto told me 87% was his best.

Going back to my model, if I use SFC of .45 it means either that my minimum drag at 110.5 mph is only 118 pounds or that my propulsive efficiency is 76% using a Catto 3-blade, cruise pitch. Neither of these conclusions seems reasonable to me. Meanwhile, it does seem reasonable that my engine with only 200 hours on it is doing what Superior and GAMI say it will do when LP 50 degF.


All of this is just in aid of trying to respond to the original suggestion that we can use drag curves. We can, but..
 
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AlexPeterson:

158kts-162kts and 7.2-7.5USgal/h = ~0.388-0.435lb/hp.h (LOP)

(this is a classic example of the need for extreme accuracy on all measurements!)

Huh? I don't follow the statement in parentheses. The largest inaccuracy in the above is assuming a certain drag coefficient, prop efficiency, weight, cg, etc. for my plane. The speeds vs fuel flows I presented were from memory, based upon hundreds of flights in all conditions, etc.. Even if the data were collected perfectly, there is going to be a range of expected variation. Just finding a stable enough air mass to do reasonable speed runs in is difficult.

The specific fuel consumption, while perhaps interesting, is not at all important to me, and is several assumptions away from TAS and fuel flow. Speed vs fuel flow is ultimately what matters, at least to me.
 
Alex, I wasn't casting criticism your way. Just trying to illustrate to Ross et al the extreme sensitivity of trying to calculate BSFC from flight data. The numbers you give seem quite reasonable estimates for flight data - you might reasonably expect to see such variation when flying S+L, but it gives you an 11-12% variation in the result - going from an expected value to an unbelievable value. I appreciate that BSFC may not be real important to youp personally.

hevans,

I took the CAFE Zero Thrust Glide Testing RV-6A model and estimated drag thrust at 199mph TAS / 176 CAS. This is the 8000' 75% value quoted by Van's. I crudely read it from the graph at 192lbf = 102hp THP. This yields a 75.5% propulsive efficiency on the Van's test aircraft. Maybe this is a more typical or realistic PE than 80-85%?

I've not seen your power and drag article before - I'll take a closer read through it when I get a chance. Looks interesting!

A
 
Yep Andy, did a ton of test flying on my 6A in the early days and fully appreciate how hard it is to get accurate data points. You need REALLY smooth air for one thing, have to wait for speeds to stabilize and it takes time to get fuel flows calibrated well through many longer flights, stop watch and filling the tanks many times. On my Subaru, there are no published limits for anything on the engine or guidelines for leaning so there was twice as much to do as on a Lycoming powered RV. As well, constant mods changed drag and tests had to be repeated later.

This was more of a ballpark, theoretical discussion, the only way to actually get a true BSFC number is on a properly calibrated dyno.

I must say it has been interesting nonetheless. I always learn something here.:)
 
Lean O' The Peak...

I flew my HR2 to Oshkosh a week early to perform project manager duties for our Fly4Life feature. It really showed off the capabilities of the Rocket and that more power can equal more efficiency.
We topped her off with 54 gallons at KZPH (FL) and I cruise climbed the mighty 540 to 10.5 and didn't land until C97, a grass strip just outside Chicago, 854NM and 4 hours later.
I burned 46.5 gallons of fuel running 20 degrees LOP with GAMI injectors and a EI ignition on one side. My estimated TAS ranged between 188 and 192 knots and GS between 195 and 205 kts with my spark advance at 33 degrees BTC, fuel burn of 10.3 gph.
Having flown my 150HP RV4 on that same route many times I got out my fuel reciepts from many moons ago and voila', nearly identical fuel amont burned but with an additional stop and more time.
Based on your above numbers, I concur. However comma as previously stated, it all boils down to distance vs time divided by $$$. :)

Smokey
HR2
www.iamanet.org
 
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We are not in total agreement yet

...

I took the CAFE Zero Thrust Glide Testing RV-6A model and estimated drag thrust at 199mph TAS / 176 CAS. This is the 8000' 75% value quoted by Van's. I crudely read it from the graph at 192lbf = 102hp THP. This yields a 75.5% propulsive efficiency on the Van's test aircraft. Maybe this is a more typical or realistic PE than 80-85%?
CAFE's report said 126 HP for 199.7 but that's THP at 7079'. I get 136.6. (They did make a mistake - confirmed by correspondence). If you move the CAFE report to 8000' you get 203 mph if you could maintain the same power. If I use 8000', 134# min. drag and 106 mph speed for best L/D then the THP for Van's 197 mph is 131.7. the drag and L/D speed are from the CAFE report.
  • If Van's got 85% propulsive efficiency then his BHP was 154.94 which would agree with my numbers for my 7A.
  • But, if Van's really did it on 75% then his propulsive efficiency would have been 131.7 out of 135 or 97.6%. No way.
  • Since the CAFE 6A performed pretty much to Van's specs, the area of disagreement is not the airplane but the 75% power number or assumption.
  • If Van's Propulsive efficiency were 75% then 131.7 THP would require 175.6 BHP.
 
Zero Thrust Glide Testing article...

I got my RV-6A drag numbers from the graph published in the CAFE ZTGT article, which looks like this:

RV-6Adragcurves.gif


I read it off (by eye) at approximately 176mph CAS, which is 199mph TAS at 8000' ISA. This is where I got the 192lbf from.

From what I can figure, you've used the data from the CAFE APR for the RV-6A - I've not even looked at that till now. Now I am scratching my head at your numbers, I have to admit! :confused:

My THP calc is 102hp (192lbf x 199mph) which is way less than either the APR's 126 or your 136, but since 75% of 180hp is 135bhp, this is where I get my 75.5% from (102/135)
 
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This gets better and better.

I got my RV-6A drag numbers from the graph published in the CAFE ZTGT article, which looks like this:

I read it off (by eye) at approximately 176mph CAS, which is 199mph TAS at 8000' ISA. This is where I got the 192lbf from.

From what I can figure, you've used the data from the CAFE APR for the RV-6A - I've not even looked at that till now. Now I am scratching my head at your numbers, I have to admit! :confused:

My THP calc is 102hp (192lbf x 199mph) which is way less than either the APR's 126 or your 136, but since 75% of 180hp is 135bhp, this is where I get my 75.5% from (102/135)
Well, we agree that I used the APR. Somehow, they don't agree. I note in passing that an RV-6A will not do 200 MPH IAS when it's at 8000'. I am not sure how to reconcile the two sets of data on the 6A. I know I'm kind of strange, but I actually think this is fun. Thank you.
 
no, not as strange as you think!

The graph goes to 200mph only because it's IAS and drag is a function of IAS, not TAS, although you need to use TAS to convert drag force to drag power.

The ZTGT graph is quite a bit different to the one featured in the RV-6A APR. Who knows which one is more accurate, but the APR published drag graph doesn't match their quoted THP at 7079' and 199.7mph.

My calcs make 199.7mph TAS = 179.9mph CAS =~220lbf (from the APR graph)= 115THP. The authors quote 126THP. I know you say there was a calculation error, but it seems 126THP isn't correct.

I'm not 100% confident I've managed to get my sums right here though...

A
 
It is worth noting that the graph that includes the Luscombe is at 1400# for both and the APR for the 6A is at 1650 or 1634 pounds. That helps explain the difference in the speed for best L/D. That affects the outcome at the other end. I think it accounts for 2.8 THP.

The graph for the Luscombe stops where the Luscombe stops so it is reasonable to assume that it stops for the 6A where it stops. The 6A in the APR had a fixed pitch wood prop on a 180 Lycoming. I just don't think that airplane can go 200 mph at standard conditions. I wonder if somehow TAS snuck in? The APR graph stops at 180 CAS. However, if we take the APR's 220 pounds of drag (not foot pounds) times 180 AS mph we get 105.6 THP. (180 mph*5280 ft/60 minutes*220 pounds/33000 foot pounds per minute). Assuming that at sea level we get 180 BHP, then the efficiency would only be 59%. For an RV, that's too low.

A second note: The TAS for best L/D changes with density altitude just as all speeds do. In other words, if the best speed for L/D CAS is 100, then at 8000' it is 112.8 TAS while remaining 100 CAS. As noted by Andy, you need TAS for THP. So if you are at 8000' DA, then the min. drag is at 112.8 on the curve. So THP at 177 at standard conditions is 99.5 THP and THP at 199.7 at 8000' is 136.59, using the same 134 pounds of minimum drag, but at adjusted TAS for the speed at which minimum drag happens.

BTW - My numbers and my E6B say that CAS for 199.7 TAS at 8000 is 177, but that's a small difference.
 
I got my RV-6A drag numbers from the graph published in the CAFE ZTGT article, which looks like this:

RV-6Adragcurves.gif


I read it off (by eye) at approximately 176mph CAS, which is 199mph TAS at 8000' ISA. This is where I got the 192lbf from.

From what I can figure, you've used the data from the CAFE APR for the RV-6A - I've not even looked at that till now. Now I am scratching my head at your numbers, I have to admit! :confused:

My THP calc is 102hp (192lbf x 199mph) which is way less than either the APR's 126 or your 136, but since 75% of 180hp is 135bhp, this is where I get my 75.5% from (102/135)

The title on this curve says that it is for 1400 lb gross weight. If we want drag at 1650 lb gross weight we need to increment the induced drag slightly. The induced drag coefficient varies with the lift coefficient. The lift coefficient varies with the weight, and with one over the square root of the speed - (this originally said it varied with the square root of the weight, but that was a huge clanger) . Thus, the lift coefficient at 162 mph at 1650 lb is the same as the lift coefficient at 176 mph at 1400 lb. Looking at the induced drag curve, we see values of 20 lb at 162 mph, and 17 lb at 176 mph. At a constant drag coefficient, drag varies as the square of the speed. So, we take the 20 lb induced drag at 162 mph, we calculate about 23.6 lb induced drag at 1650 lb at 176 mph CAS. This is about 6.6 lb higher than the value on this curve for 1400 lb.

This takes the total drag up to about 199 lb, or about 106 thp. This still differs quite a bit from the values from the CAFE APR, so there is more to the story somewhere. They may have discovered errors in the original data. I'd tend to give more credence to the data that was published later.
 
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Big OOPS

Boy, is my face red. There was an error in my spreadsheet model. I still cannot account for the differences between version of the same 6A tested by the same CAFE, probably on the same occasion.

That said, my numbers were wrong. Andy was right as far as I can tell.

Needless to say, the model has been fixed, should anyone want to use it. It's linked in the article.
 

That said, my numbers were wrong. Andy was right as far as I can tell.

That might be a risky assumption at this stage, Howard! :eek: I understand your feelings though as I too found a huge clanger in one of my own spreadsheets this afternoon.

Anyway, I'm a little wiser after this thread too. Thanks Kevin for adding your post - it highlighted an incorrect assumption of my own.

A
 
Thanks Kevin for adding your post - it highlighted an incorrect assumption of my own.
I hope you were looking at my math, and not at my words, because my original post had a major screw up in the wording. The math was right, but the description of the math was wrong. I fixed it a few minutes ago. First mistake this year :)