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  #21  
Old 06-10-2010, 08:34 AM
hevansrv7a's Avatar
hevansrv7a hevansrv7a is offline
 
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Location: Detroit, MI
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Default Better, Much Better

Here is a spreadsheet which implements Paul's formula for the Superior IO-360+ (180 HP).

Here is the chart for that engine.

The low and mid power error is in the low 4% range. The higher power error is less than 1%. Pretty good. I arbitrarily set the constant for the 75% value.

There is no temperature nor altitude correction built into this one. The user can insert columns or rows for other intervals of MAP or RPM and copy the formula from adjacent cells.

Let's see how it works on some other engines.
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  #22  
Old 06-11-2010, 04:39 AM
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Kevin Horton Kevin Horton is offline
 
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Location: Ottawa, Canada
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Quote:
Originally Posted by elippse View Post
Well, I think I may have come up with a reasonably simple and fairly accurate method of determining engine power from rpm and MAP. I did these calculations using engine data sheets from an O-235 L2C, an O-320B, and an O-320D. Keep in mind that these engine power graphs are not exact, they are based on estimates from various tests. Look at the lines on the graph from an angle and on some data sheets most of the lines are parallel and some converge at a distant point, and some even have some lines parallel and one or two others angled! Go figure! But they never measured the engine horsepower in flight at all of these altitudes and at all of these rpm and MAP values. They were based on engineering estimates. The sea-level numbers, of course, were probably obtained from tests on engines in a test cell operated at these various rpm and MAP, and then corrected to sea-level MAP and temperature. Do you really think they waited for a 59F day at 29.9213" pressure, or had a sealed test cell where they maintained the temperature and pressure inside the cell to a very high accuracy? No, they used correction factors with the measured torque, rpm, pressure, and temperature just as do all of the engine makers with their dynos except the aircraft engine data was probably reduced with slide rules whereas all of the new dynos do it with built-in computers. As far as the formula for power, here's what you do: first subtract the MAP from the engine's sea-level MAP at rated power, then multiply this remainder by an engine-related constant. Subtract this new value from the SLMAP and divide this by the SLMAP. Multiply this by the actual rpm and divide by the rated rpm. Multiply this by 100 to get percentage of power. You can further refine this for inlet temperature as given previously. For my O-235, SLMAP is 28.4", rated rpm is 2800, and the constant is approximately 1.4. This constant can be calculated for each engine from the data sheet. This probably isn't the untarnished silver bullet (Lone Ranger's?) that Howard was looking for, but it probably comes very close, maybe as close as the original engineering estimates!
Keep in mind that the relationship between rpm and power is not necessarily linear. For example, the angle-valve Lycomings have a tuned induction system that helps them make more power than the angle valve engines, but this is only working well at high rpm. The advantage of the tuned induction system whithers away as the rpm decreases, and somewhere around 2300 rpm the two engines make the same power. At lower rpm the parallel valve engine is actually more powerful.

For example, power at 28.6" MP at sea level, std temp:
rpm IO360A O360A
2100 147.1 152.7
2200 154.6 161.1
2300 165.6 166.4
2400 174.8 171.7
2500 183.2 175.9
2600 192.6 180.1
2700 200.0 183.1


At 24" MP at sea level, std temp:
rpm IO360A O360A
2100 117.3 120.1
2200 123.4 126.7
2300 132.1 131.2
2400 139.2 135.7
2500 146.2 139.0
2600 153.5 142.3
2700 160.1 145.3
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Last edited by Kevin Horton : 06-11-2010 at 10:44 AM.
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  #23  
Old 06-11-2010, 09:49 AM
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rv6ejguy rv6ejguy is offline
 
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Location: Calgary, Canada
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In Kevin's example the IO has torque peak at around 2600/2700 rpm while the O peaks at 2200 rpm. Torque peak coincides with maximum volumetric efficiency. A linear hp relationship only exists where the VE is the same at all rpms and frictional and pumping losses are linear or where VE increases offset other losses- which they rarely do.

The torque curve is remarkably flat on these engines, varying only about 6% in the case of the IO across the rev range. The IO hp numbers here indicate a straight linear change with rpm while the O numbers do not. It may be safe to surmise that on engines which have the hp and torque peaks at nearly the same rpm (and up high in the rev range), a near linear hp progression with rpm within a narrow rpm band is possible. On engines with torque peak occurring lower in the rev range as with the O example, it is not possible to have a linear progression with rpm due to higher frictional losses and a simultaneous loss in VE as rpm rises.

As far as humidity effects go, very high humidity in high ambient temperature conditions can reduce power output by almost 4% compared to a less than standard day with no humidity. Very few places have 0% humidity but it is easy to have a 1.5-2% error in normal flying conditions without taking humidity effects into consideration. Dynos always take dry and wet bulb readings to correct hp for humidity.

So again, this is why engines are validated on dynos. There are just so many variables to consider that a simple math model with limited information is probably not too accurate, especially when an existing engine is used as a baseline and changes have been made to various things like induction, exhaust and ignition. The more assumptions that are made, the less accurate the model generally. Any model which does not take temperature, humidity and altitude into effect is more useful for theoretical discussions as worst scenario cases could result in errors of easily 10%.

Where more information is available like camshaft timing, cylinder head airflow, bore to stroke ratios, connecting rod length, induction and exhaust specs etc. fairly accurate math models are available today to predict hp from a given engine configuration in the racing world. A low cost example of this type of software is here: http://www.quarterjr.com/engine_jr.htm There are many other more expensive and complex programs available.

A fascinating subject...
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Turbo Subaru EJ22, Marcotte M-300, IVO, RV6A C-GVZX flying from CYBW- 379 hrs. on the Hobbs, new ventral rad installed, new systems and mods, flight testing now
Twin Turbo Subaru EG33, Marcotte M-300, MT, RV10- Tail is on, stalled by life and work.

Last edited by rv6ejguy : 06-11-2010 at 10:16 AM.
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  #24  
Old 06-11-2010, 11:13 AM
elippse elippse is offline
 
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Location: Arroyo Grande, CA
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Default Power calcs

As pointed out by Ross and others, the power an engine produces is such a tangled web of so many components that the only method I'm aware of to know what your power is in flight is to have a torque sensor on the propeller shaft and use this with rpm to calculate power. What I tried to present was a short-hand method to arrive at a power estimate that you could use to compare with the number that the came out of the avionic's power estimate. Notice the operative word: ESTIMATE! Maybe we could get Saber to integrate a wireless torque strain-gage in their prop extension and use that, along with rpm and a simple micro-processor to give us true horsepower. Now all we would need is a thrust sensor in the extension too, and that, with TAS to compute thrust power, would tell us prop efficiency! Ok, guys! Here's a business opportunity!
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  #25  
Old 06-11-2010, 11:35 AM
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rv6ejguy rv6ejguy is offline
 
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Quote:
Originally Posted by elippse View Post
As pointed out by Ross and others, the power an engine produces is such a tangled web of so many components that the only method I'm aware of to know what your power is in flight is to have a torque sensor on the propeller shaft and use this with rpm to calculate power. What I tried to present was a short-hand method to arrive at a power estimate that you could use to compare with the number that the came out of the avionic's power estimate. Notice the operative word: ESTIMATE! Maybe we could get Saber to integrate a wireless torque strain-gage in their prop extension and use that, along with rpm and a simple micro-processor to give us true horsepower. Now all we would need is a thrust sensor in the extension too, and that, with TAS to compute thrust power, would tell us prop efficiency! Ok, guys! Here's a business opportunity!
I like Paul's idea of actual in flight torque measurement combined with some additional information- this would allow you to develop an accurate math model for that particular engine. That would be a most interesting project!
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Ross Farnham, Calgary, Alberta
Turbo Subaru EJ22, Marcotte M-300, IVO, RV6A C-GVZX flying from CYBW- 379 hrs. on the Hobbs, new ventral rad installed, new systems and mods, flight testing now
Twin Turbo Subaru EG33, Marcotte M-300, MT, RV10- Tail is on, stalled by life and work.
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  #26  
Old 06-11-2010, 04:23 PM
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hevansrv7a hevansrv7a is offline
 
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Location: Detroit, MI
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Lightbulb Project for the day

I don't have any idea how to put a torque sensor on the airplane in flight, but here is an idea for validating at least one or a few points on the curves. I have not worked out the practical aspects yet. Who will try this?

1. Build some L shaped chocks big enough for next step.
2. Put aircraft scales on the chocks.
3. Put the airplane on the scales. The chocks are now holding the airplane on the scales because they extend vertically enough.
4. Tie back the airplane using the mains high on the legs.
5. Record the weights on the three scales.
6. For various RPM's, static, record the RPM and the MAP as well as temp, pressure altitude and any other variable you can name. Record the weights for each data point. For CS props, try with combinations of MAP and RPM.
7. At any time, measure the distances from the center of the plane to the center of the contact patch of the tire.
8. Using the arm you measured and the change in weights on the mains (did weight on tail/nose change too?) compute the torque.
9. Compute the BHP from the torque and the RPM for each data point.
10. Compare to the manufacturer's chart.
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We can lift ourselves out of ignorance, we can find ourselves as creatures of excellence and intelligence and skill. We can be free! We can learn to fly!" -J.L. Seagull
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  #27  
Old 06-11-2010, 08:06 PM
elippse elippse is offline
 
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Quote:
Originally Posted by hevansrv7a View Post
I don't have any idea how to put a torque sensor on the airplane in flight, but here is an idea for validating at least one or a few points on the curves. I have not worked out the practical aspects yet. Who will try this?
I wrote about this method several years ago and it was published somewhere. We tried this on my friend's gyro and got fairly good results. About 2 years ago I had a friend read the scales while I managed the throttle on my plane; the results weren't too good as any slight variation in wind caused enough jiggling of the scales that they couldn't be read reliably. Digital scales were even worse than bathroom scales because the numbers jumped about so much that there was no way to even get an eyeball average of what they displayed! We did get a good WOT thrust number from the spring scales we connected from the main gear legs to a car nearby with 1/8" cables. There are two distance measurements that must be taken into account. The first is the radial distance from the crank centerline to the tire contact patch, and the second is the horizontal distance from one tire to the other. The force normal (perpendicular) to the radius, the torque, must be calculated from the angle that the radii make with the horizontal distance, resolving the force on the scale, and then this used with the radial distance to estimate the torque, then that used with rpm to get the horsepower. I have a formula and drawing somewhere illustrating this method. I think I called this the "poor man's dyno!". BTW; it might be possible to use the RFID technology to wire-less transmit the rotating torque and thrust data.

Last edited by elippse : 06-11-2010 at 08:11 PM. Reason: BTW thought
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  #28  
Old 06-12-2010, 07:04 AM
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hevansrv7a hevansrv7a is offline
 
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Quote:
Originally Posted by elippse View Post
I wrote about this method several years ago and it was published somewhere. We tried this on my friend's gyro and got fairly good results. About 2 years ago I had a friend read the scales while I managed the throttle on my plane; the results weren't too good as any slight variation in wind caused enough jiggling of the scales that they couldn't be read reliably. Digital scales were even worse than bathroom scales because the numbers jumped about so much that there was no way to even get an eyeball average of what they displayed! We did get a good WOT thrust number from the spring scales we connected from the main gear legs to a car nearby with 1/8" cables. There are two distance measurements that must be taken into account. The first is the radial distance from the crank centerline to the tire contact patch, and the second is the horizontal distance from one tire to the other. The force normal (perpendicular) to the radius, the torque, must be calculated from the angle that the radii make with the horizontal distance, resolving the force on the scale, and then this used with the radial distance to estimate the torque, then that used with rpm to get the horsepower. I have a formula and drawing somewhere illustrating this method. I think I called this the "poor man's dyno!". BTW; it might be possible to use the RFID technology to wire-less transmit the rotating torque and thrust data.
I don't recall that write-up, but I guess great minds do think alike (said with an exaggerated sense of self-worth). I do recall in an EAA article a method of testing the engine on a test stand with a long arm and a scale. On-aircraft is a little trickier. Just a note that static thrust is pretty much meaningless, but the torque measurement, if well done, will give a sound basis for BHP. Good point about needing to draw the triangle to get the torque measurement correct.

It is worth noting that the results of such a measurement can be compared to the the manufacturer's curves so that they can be viewed realistically. Some have noted that there may be a "loss" factor for accessories, etc. when comparing reality to test cell. In other words, my 180 HP engine may not really put 180 BHP to the prop. We also don't know that all engine curve test cell procedures are equal; it is likely they are not.

The variables noted by rv6ejguy above affect the undependable relationship of the curves vs. the reality, but we are still trying to get a formula that matches what the manufacturer says. Both valid, but entirely different issues.
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We can lift ourselves out of ignorance, we can find ourselves as creatures of excellence and intelligence and skill. We can be free! We can learn to fly!" -J.L. Seagull
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