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  #61  
Old 05-22-2009, 12:37 PM
Kevin Horton's Avatar
Kevin Horton Kevin Horton is offline
 
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Quote:
Originally Posted by Steve Brown View Post
I don't have a fuel flow gauge on my airplane. However, back in the early 90s I did some very careful observation of indicated airspeed verses power settings in my Mooney. I didn't use the Mooney power schedule, I used the Lycoming schedule which was very detailed in terms of RPM, MP, and air temperature.

What I found was that within very small variation, if I had the same power setting I had the same IAS. This was independent of OAT, RPM, and altitude.

How accurate is this method? I'm sure there are inaccuracies because I can think of some potential problems right up front. Nevertheless, I thinks its close enough to address this subject.
Interesting observation. I'm certainly not going to say you didn't see what you saw, because you were there and I wasn't. But, it is hard to reconcile your observations against theory. Do you recall the range of altitudes you would have been at when you made these observations? Do you recall roughly how repeatable the IAS was for a given percent power?

Accepted theory says that profile drag is proportional to the square of the equivalent airspeed. In the speed and altitude range that most RVers care about, equivalent airspeed = calibrated airspeed for all practical purposes. Ignoring ASI instrument error and static system position error, calibrated airspeed = indicated airspeed. So, roughly speaking, profile drag is proportional to IAS^2.

Engine power times prop efficiency = drag times TAS. But, for a given TAS, the IAS will decrease as we climb, which causes the drag to decrease. So, for a given power, as we climb, the TAS will increase, but the IAS should decrease. To give you an idea of the rough relationships that conventional theory predicts, here are the results of some very rough cruise performance testing done on my RV-8, with old Hartzell prop. The predicted speeds at 65% power, standard day, 1600 lb are:

Code:
Altitude  TAS   CAS
 (ft)    (kt)  (kt)
 4000    167.5 158.0
 6000    170.6 156.2
 8000    173.7 154.3
10000    176.9 152.5
Between 4000 ft and 10000 ft, we see a 9.4 ft increase in TAS, and a 5.5 kt decrease in CAS. So while neither TAS nor CAS are constant with power, CAS is more constant than TAS.

But, this is theory. YMMV. As Yogi Berra supposedly said "In theory there is no difference between theory and practice. In practice there is. " Changes of prop efficiency as power, rpm and TAS change could muck things up slightly.
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  #62  
Old 05-22-2009, 01:39 PM
Steve Brown Steve Brown is offline
 
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Default Its drag

Quote:
Originally Posted by Kevin Horton View Post
Interesting observation...... Do you recall the range of altitudes you would have been at when you made these observations? Do you recall roughly how repeatable the IAS was for a given percent power?

Accepted theory says that profile drag is proportional to the square of the equivalent airspeed. ...... So, roughly speaking, profile drag is proportional to IAS^2.

Engine power times prop efficiency = drag times TAS.....
Those were my observations, but the details are fuzzy. I extracted the data from lycoming graphs and did some curve fitting with excel. Then used the curve fit data to make myself a more better power schedule. Inputs were RPM, MP, and air temp in kelvins.

I did not do a documented study, I just noticed that whenever I had the same power setting, I had the same IAS.

I agree drag is roughly proportional to IAS^2. So, if you have the same IAS, you have the same drag. Therefore, the same work is being done. Thus you are at the same power setting. I think this makes the point.

If you move between two different IAS the induced drag (due to AOA) changes so you cannot solve it that simply.

Drag related to potentially differing prop RPM are not accounted for in this simplistic approach. There may be other errors, but I think its decently correct.

you lost me in this: engine power x prop efficiency = drag x TAS

I would have thought that TAS term should be IAS. I'm not saying its wrong, I just don't understand it.
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  #63  
Old 05-22-2009, 02:16 PM
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Default Drop in IAS

Kevin and Steve,

While I was measuring the peak EGT and fuel flow rate, I also recorded the indicated air speed.

Interesting that on 2 separate runs, then IAS starts to drop slightly just as you reach peak (2 knots). Even more interesting that you also get a slight increase (2 knots) almost exactly at 75 ROP and then drops off that slight amount as you go richer.

I did order 1 new restrictor from Airflow which should put my spread less than 0.2 gal/hr.
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  #64  
Old 05-22-2009, 02:24 PM
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Kevin Horton Kevin Horton is offline
 
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Quote:
Originally Posted by Steve Brown View Post
I agree drag is roughly proportional to IAS^2. So, if you have the same IAS, you have the same drag. Therefore, the same work is being done. Thus you are at the same power setting. I think this makes the point.
All true, except you need to replace IAS with TAS. If you have a given amount of drag, the power required is equal to TAS times drag (with appropriate unit conversions). So, power required varies with TAS times drag, with drag varying with IAS^2, so power varies with TAS * IAS^2. But, the relationship between TAS and IAS varies with altitude, so in theory, the IAS we get for any given power should also vary with altitude.

Quote:
Originally Posted by Steve Brown View Post
you lost me in this: engine power x prop efficiency = drag x TAS
The point was that from an aerodynamic point of view, it is thrust power that matters. Thrust power is the power that is actually transmitted by the prop to the airflow. It is equal to engine power times propeller efficiency. Prop efficiency will be relatively constant over the range of normal cruise conditions, so we can ignore it. But if we starting making big changes in altitude, power, rpm, etc, then the prop efficiency will be changing, and this will affect any predictions we attempt to make.

Anyway, I'm not arguing against your observations, on that aircraft, with that engine, prop, ASI, etc. But I doubt they point to any general conclusion that we can apply to other aircraft.
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  #65  
Old 05-23-2009, 10:41 AM
Steve Brown Steve Brown is offline
 
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Default Got it

Quote:
Originally Posted by Kevin Horton View Post
........ So, power required varies with TAS times drag, with drag varying with IAS^2, so power varies with TAS * IAS^2. .........
Kevin,

Thanks for straightening me out. Put that way it's more clear:
work = force x distance

force proportional to IAS^2, distance proportional to TAS. So your assertion must be true.

That has me wondering about my early 90s observations which must be incorrect. As you say, I must have stumbled on to some conditions which roughly canceled the error. Whoops

Anyway, back to finding power when LOP

All of the information needed is in TAS, IAS, and the ROP power schedule, but drag does not exactly follow IAS^2 due to AOA. How significant is this?

The few knot IAS difference I get in my airplane going from full fuel to very low fuel on a long trip say it might be significant. The 1 mph difference between light and heavy on the vans web site say not so much. This may be another case of faulty observations.

I seems like mapping IAS^2 x TAS against the ROP power schedule should yield a solution in which given IAS^2 x TAS power is always known regardless of mixture setting. That is, at least over the relatively narrow range of normal cruise speeds. At much lower speeds the power is so low it doesn't matter how you lean and at much higher speed you should not be running LOP.

Please comment.
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Last edited by Steve Brown : 05-23-2009 at 10:42 AM. Reason: error
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  #66  
Old 05-23-2009, 11:43 AM
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Ron Lee Ron Lee is offline
 
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At higher speed you can run LOP IF the manifold pressure/percentage horsepower is low enough, which it is where I fly.
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  #67  
Old 05-23-2009, 03:00 PM
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Kevin Horton Kevin Horton is offline
 
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Quote:
Originally Posted by Steve Brown View Post
Anyway, back to finding power when LOP

All of the information needed is in TAS, IAS, and the ROP power schedule, but drag does not exactly follow IAS^2 due to AOA. How significant is this?

The few knot IAS difference I get in my airplane going from full fuel to very low fuel on a long trip say it might be significant. The 1 mph difference between light and heavy on the vans web site say not so much. This may be another case of faulty observations.
As you note, there are other factors that come into play. Weight and CG for example. At a given weight and power, you'll go slightly faster at aft CG than you would at forward CG. I suspect the difference is on the order of 2 kt over the full CG range. Weight - my model suggests that at 75% power at 8000 ft the IAS would increase about 1 kt for every 100 lb reduction in weight. At lower power cruise and higher altitudes, the effect of weight will be slightly greater, as the power required vs speed curve gets flatter as you more closer to IAS for minimum power.

Quote:
I seems like mapping IAS^2 x TAS against the ROP power schedule should yield a solution in which given IAS^2 x TAS power is always known regardless of mixture setting. That is, at least over the relatively narrow range of normal cruise speeds. At much lower speeds the power is so low it doesn't matter how you lean and at much higher speed you should not be running LOP.

Please comment.
We can come up with all kinds of nice theoretical relationships between speed and power, but I'm not sure they are usable in the real world in the way you want. I.e., I don't think it is practical to say "if you want 75% power, set the power to get a speed of XXX kt IAS". First, even at a given altitude, the relationship between speed and power is affected by weight, CG and temperature, with each of those possibly affecting things by a couple of knots. Second, it takes quite some time after setting power for the speed to stabilize. Third, the air is never perfectly calm. Even on the nicest of days, there will be small perturbations that cause the airspeed to wander up and down a few knots.

I think it is much more practical to simply set power with respect to rpm, MP and fuel flow.

I may regret posting this, as it'll raise more questions than it answers, but for the terminally technically inclined, several weeks ago I was playing around with some mathematical analysis software, and while I was experimenting to see what it could do, I put together a page which looked at the technical details of cruise performance analysis (if my server is down, there is another copy here). It isn't really usable in its current form, but I will eventually write a much less technical Kitplanes article, with accompanying spreadsheet. The pages have a lot of technical goblity gook about cruise performance, then several graphs showing the results of analyzing cruise performance from one flight on my RV-8. The graphs near the end show the predicted effect of weight, altitude and temperature on the relationships between power required and TAS.
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  #68  
Old 05-23-2009, 05:01 PM
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hevansrv7a hevansrv7a is offline
 
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Default Finding power while LOP

The thread raises lots of other interesting points. Some so interesting that I had to correct my "model". Thanks again, Kevin.

The question was about finding power while LOP, right? As said above:
Finding power while LOP is best done not from MAP and RPM per the Lyc charts but from fuel flow. Walter Atkinson and the GAMI guys have shown that when there is excess air (that defines LOP) your SFC is about 0.40. Said another way, if you multiply your fuel flow in gallons per hour by 14.9 you will get your BHP. (Your THP is your BHP times your prop efficiency but you really don't care about that in this application.) You cannot do it with MAP and RPM and altitude if you are LOP.

0.40 pounds per horsepower per hour
times
6.0 pounds per gallon (actually varies with temp)
means
6.0 / .40 = 15 horsepower per gallon per hour.
Example: 8 gph times 15 = 120 HP which is 67% for a 180 HP engine.

Acccording to Walter, RPM, MAP and altitude may vary but this relationship will be "pretty doggone accurate".
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  #69  
Old 05-24-2009, 09:58 AM
rwhittier rwhittier is offline
 
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Default It works pretty well on my 6 Cyl TCM...

As others have posted, I am not sure why you are seeing anything different. This formula is not cylinder specific - its piston engine physics. Air and Fuel mixtures burn well in a range that is well understood in piston engines and it doesn't change. The actual formula is 14.9 X FF = HP when LOP. I use 15 because it gets me within 1 or 2 HP on my IO-550 - which is close enough for me. Plus I can do it in my head

The original research on this stuff dates back many decades. The APS course relies heavily on two books written in the 50's from work done back into the 30's. As you can imagine at that time it mostly was done on radials - some quite large radials with many more than 6 cylinders. One book, published in 1957 is collaborative work between American Airlines (at the time operating DC-7's) and Curtis-Wright. APS says "It is a remarkable little book that very clearly and concisely explains the principles behind mixture control in ALL internal combustion, spark-fired, gasoline engines." They sell the book on their website along with another one published by Pratt and Whitney. Anyone really interested in this stuff ought to read them.



Quote:
Originally Posted by Geico266 View Post
This may work for a 4 cylinder, but it doesn't work for a 6.
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  #70  
Old 05-24-2009, 12:28 PM
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Kevin Horton Kevin Horton is offline
 
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Quote:
Originally Posted by rwhittier View Post
As others have posted, I am not sure why you are seeing anything different. This formula is not cylinder specific - its piston engine physics. Air and Fuel mixtures burn well in a range that is well understood in piston engines and it doesn't change. The actual formula is 14.9 X FF = HP when LOP. I use 15 because it gets me within 1 or 2 HP on my IO-550 - which is close enough for me.
The old Lycoming info I have certainly suggests that 14.9 X FF = HP when LOP isn't too far off the mark. The exact answer you get from this old Lycoming analysis technique varies a bit depending on rpm, compression ratio, power setting, and how far LOP you are, but usual results seem to be in the range of 14.5 X FF to 14.7 X FF. But, given typical accuracy of FF indications, there is nothing wrong with rounding up to 15.

Here is an example of the relationship between fuel flow, power, power/FF and bSFC for an IO-360 at 2400 rpm, with 8.7 compression ratio, and a power setting that resulted in 9 GPH at peak EGT:

Code:
 Fuel   Pwr    Pwr      bSFC
 Flow          per          
               GPH          
(GPH)  (hp) (hp/GPH) (lb/h/hp)
 6.0   38.6    6.43     0.934                        
 6.1   44.7    7.33     0.820                        
 6.2   50.6    8.16     0.737                        
 6.3   56.2    8.92     0.674                        
 6.4   61.5    9.61     0.625                        
 6.5   66.6   10.24     0.587                        
 6.6   71.4   10.82     0.556                        
 6.7   76.0   11.34     0.530                        
 6.8   80.3   11.81     0.509                        
 6.9   84.4   12.23     0.491                        
 7.0   88.3   12.61     0.476                        
 7.1   92.0   12.95     0.464                        
 7.2   95.4   13.26     0.453                        
 7.3   98.7   13.52     0.445                        
 7.4  101.8   13.75     0.437                        
 7.5  104.6   13.95     0.431                        
 7.6  107.3   14.12     0.426                        
 7.7  109.8   14.26     0.421                        
 7.8  112.2   14.38     0.418                        
 7.9  114.4   14.48     0.415                        
 8.0  116.4   14.55     0.413                        
 8.1  118.3   14.60     0.412                        
 8.2  120.0   14.63     0.411                        
 8.3  121.6   14.65     0.410  Fuel flow for best efficiency
 8.4  123.0   14.65     0.410                        
 8.5  124.4   14.63     0.411                        
 8.6  125.6   14.61     0.411                        
 8.7  126.7   14.57     0.413                        
 8.8  127.7   14.51     0.414                        
 8.9  128.6   14.45     0.416                        
 9.0  129.5   14.38     0.418  Fuel flow for peak EGT
 9.1  130.2   14.31     0.420                        
 9.2  130.8   14.22     0.423                        
 9.3  131.4   14.13     0.425                        
 9.4  131.9   14.04     0.428                        
 9.5  132.4   13.94     0.431                        
 9.6  132.8   13.84     0.434                        
 9.7  133.2   13.73     0.438                        
 9.8  133.5   13.62     0.441                        
 9.9  133.8   13.52     0.445                        
10.0  134.1   13.41     0.448                        
10.1  134.3   13.30     0.452                        
10.2  134.6   13.19     0.456                        
10.3  134.8   13.09     0.459                        
10.4  135.0   12.99     0.463                        
10.5  135.3   12.88     0.466                        
10.6  135.4   12.77     0.471  Fuel flow for best power
10.7  135.4   12.65     0.475                        
10.8  135.4   12.54     0.479                        
10.9  135.4   12.42     0.484                        
11.0  135.4   12.31     0.488                        
11.1  135.4   12.20     0.493                        
11.2  135.4   12.09     0.497                        
11.3  135.4   11.98     0.502                        
11.4  135.4   11.88     0.506                        
11.5  135.4   11.77     0.511                        
11.6  135.3   11.66     0.515                        
11.7  135.2   11.56     0.520                        
11.8  135.1   11.45     0.525                        
11.9  135.0   11.34     0.530
Points of interest:

The best efficiency is with a fuel flow that is about 0.6 to 0.7 GPH lean of peak EGT. If you go leaner than that, the hp per fuel flow starts to drop. At this condition, the power is about 9% less than peak power, but the fuel flow has dropped about 22% from the fuel flow for peak power. The efficiency, in terms of fuel required to produce one hp, is about 13% better than at mixture for best power.

If you get too lean, the power and efficiency fall off very quickly. In my experience you can sense this, as the engine starts to run rough, and the IAS falls off quick significantly.

The Lycoming data suggests that there is wide band of fuel flows around peak power mixture where the power is essentially constant.
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