Determining the maximum endurance speed
I get the impresson people are trying to overcomplicate a relatively simple answer to a relatively simple question vis "How to experimentally determine max endurance speed in a piston engine aircraft?" Fuel flow for practical purposes is ~proportional to power in a piston engine so:
Go flying on the smoothest, most calm day you can find. In level flight, progressively & slowly reduce power to reduce speed until level flight can only just be maintained. Any slower and more power will be required to maintain levle flight so the aircraft must be flying at Vmp. Whilst FF is not exactly proportional to power it's close enough to give a workable solution.
Add in the usual caveats about mixture leaned, an oversquare MP/RPM combination if possible, minimum drag configuration, aft CG, light weight, low density altitude and the like.
To correct something the original poster described in his or her method: It's not correct to increase power at the point where there is a greater proportional reduction in speed for a given amount of power reduction. If it can fly S&L at that lower power setting then *any* increase in power setting moves you further away from Vmp. It doesn't matter how much the speed reduces per unit of power reduction - what matters is finding the minimum power with which you can maintain level flight irrespective of the eventual speed. You should find, however, that once in the region of the bottom of the power curve you can make a small increase in power with a correspondingly small increase in fuel flow but realise a proportionally large gain in speed. Won't be at Vmp any more but the difference is small.
Go flying on the smoothest, most calm day you can find. In level flight, progressively & slowly reduce power to reduce speed until level flight can only just be maintained. Any slower and more power will be required to maintain levle flight so the aircraft must be flying at Vmp. Whilst FF is not exactly proportional to power it's close enough to give a workable solution.
Add in the usual caveats about mixture leaned, an oversquare MP/RPM combination if possible, minimum drag configuration, aft CG, light weight, low density altitude and the like.
To correct something the original poster described in his or her method: It's not correct to increase power at the point where there is a greater proportional reduction in speed for a given amount of power reduction. If it can fly S&L at that lower power setting then *any* increase in power setting moves you further away from Vmp. It doesn't matter how much the speed reduces per unit of power reduction - what matters is finding the minimum power with which you can maintain level flight irrespective of the eventual speed. You should find, however, that once in the region of the bottom of the power curve you can make a small increase in power with a correspondingly small increase in fuel flow but realise a proportionally large gain in speed. Won't be at Vmp any more but the difference is small.
Last edited by Tinstaafl; 21st Jan 2009 at 19:41.
Go flying on the smoothest, most calm day you can find. In level flight, progressively & slowly reduce power to reduce speed until level flight can only just be maintained. Any slower and more power will be required to maintain levle flight so the aircraft must be flying at Vmp.
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Fuel flow for practical purposes is ~proportional to power in a piston engine
Also it isn't strictly proportional, because there are fixed losses. Look at any fuel flow v. HP chart and you see that at zero HP there is still a considerable fuel flow. It is this fixed loss (which is actually related to RPM and probably other second order stuff) which makes most of the traditional flight equations less than useful for powered flight.
Fuel flow is the better way but one needs to have an accurate FF meter to do it that way. Outcome is pretty much the same using power setting though.
While it doesn't really matter if power is proportional to fuel flow (as long as it's a monotonic function), you do have to have a way of knowing that you have the same power, more power or less power at different times (i.e. when you're trying out different speeds). I would worry that issues like propeller efficiency differences with speed make that difficult to assess. The differences may be small, but the differences in power required with speed are actually also quite small around best endurance speed.
But I haven't done the experiment and you may well be right that FF is not practically required.
why do you want to know the greatest endurance speed? Surely the more useful thing to know is the best fuel economy speed which, as someone else has posted, requires you to know Groundspeed and fuel flow rate. Staying airborne for hours on end does not guarantee you have covered the biggest distance on the tank full of fuel. You need to fly faster than normal best economy airspeed if you have a headwind and slower if you have a tailwind. This is very noticeable at the normal cruise speed of my Rans, 65 to 70 MPH.
Andrew.
Andrew.
The experiment...
Fixed pitch, caburettor?
Maintaining height:
Reduce throttle (reduces fuel flow) as far as possible.
Lean to max rpm (reduces fuel flow)
Repeat until fuel flow is minimal still maintaining height.
NB this maximises endurance. It may not be good for the engine, or for safety, or anything else. It single-mindedly maximises endurance on the assumption that endurance is limited by fuel running out.
Maintaining height:
Reduce throttle (reduces fuel flow) as far as possible.
Lean to max rpm (reduces fuel flow)
Repeat until fuel flow is minimal still maintaining height.
NB this maximises endurance. It may not be good for the engine, or for safety, or anything else. It single-mindedly maximises endurance on the assumption that endurance is limited by fuel running out.
Moderator
why do you want to know the greatest endurance speed? Surely the more useful thing to know is the best fuel economy speed which, as someone else has posted, requires you to know Groundspeed and fuel flow rate. Staying airborne for hours on end does not guarantee you have covered the biggest distance on the tank full of fuel.
Endurance would be the same as "best fuel economy speed", which does not require that you know the groundspeed, as best fuel economy speed would be an airspeed, not a groundspeed. If you are flying for best fuel economy, you do not care about getting somewhere quickly, so groundspeed is not a factor.
Once you have determined the best speed for endurance or economy, you may be able to reduce the fuel flow by leaning. doing that will not affect the speed, but will improve the endurance/economy.
Agreed, staying airborne for hours does not guarantee that you have covered the greatest distance, because you wern't flying at enduarance to cover the greatest distance. You were flying at endurance speed to stay away from earth as long as possible, perhaps to observe for as long as possible (search), or wait for conditions on earth to change, so you can return (blocked runway).
You would want to know the best speed for endurance for an aircraft you fly, because that speed is one of the values which is important for safe operation in unusual circumstances. Sure, there are other more interesting speeds to know for your plane, but it does not diminish the importance of this one!
Pilot DAR
Pilot DAR, I was sort of with you until the end of the second paragraph when you said "If you are flying for best fuel economy, you do not care about getting somewhere quickly, so groundspeed is not a factor."
This is completely wrong. Take the case where the headwind is the same as the airspeed, you will burn all of the fuel in the tank and still be where you started from. Zero MPG. However If you open the throttle a tad more, fuel consumption (ltrs per hour) will go up a bit, groundspeed will have a value greater than zero and voila! MPG will have a value, albeit a low value, but progress is made for the fuel consumed.
In my Rans I get through about 11 ltrs an hour at 55 mph, 15 ltrs an hour at 70 mph and 20 ltrs an hour at 85 mph. So in still air at 55 mph a ltr of fuel takes me 5 miles. At 70 mph a litre of fuel takes me only 4.6 miles and at 85 miles an hour a ltr of fuel takes me just 4.25 miles. 55 mph is clearly the best economy speed.
Now see what happens when there is a headwind of, say, 30 mph. At an airspeed of 55 mph the groundspeed is now down to (55-30) = 25 mph. A ltr of fuel now takes me just (25/11) = 2.27 miles. If I push the throttle open a bit and raise the airspeed to 70 mph the groundspeed rises to 40 mph. A ltr of fuel takes me (40/15) = 2.67 miles at 70 mph. If I open the throttle a bit more and raise the airspeed to 85 mph the groundspeed rises to 55 mph and the ltr of fuel now takes me (55/20) = 2.75 miles. So when there is a good headwind you need to fly faster than the most economical still air airspeed for best economy. Now 85 mph is the best airspeed for fuel economy.
For a 10 mph headwind the figures for 55, 70, 85 mph are 4.1 miles per ltr, 4.0 and 3.7 so 55 mph is the best airspeed still.
For 20 mph headwind the figures are 3.2, 3.33 and 3.25 so 70 mph is the best economy airspeed.
Andrew.
These are real figures from a real aircraft.
This is completely wrong. Take the case where the headwind is the same as the airspeed, you will burn all of the fuel in the tank and still be where you started from. Zero MPG. However If you open the throttle a tad more, fuel consumption (ltrs per hour) will go up a bit, groundspeed will have a value greater than zero and voila! MPG will have a value, albeit a low value, but progress is made for the fuel consumed.
In my Rans I get through about 11 ltrs an hour at 55 mph, 15 ltrs an hour at 70 mph and 20 ltrs an hour at 85 mph. So in still air at 55 mph a ltr of fuel takes me 5 miles. At 70 mph a litre of fuel takes me only 4.6 miles and at 85 miles an hour a ltr of fuel takes me just 4.25 miles. 55 mph is clearly the best economy speed.
Now see what happens when there is a headwind of, say, 30 mph. At an airspeed of 55 mph the groundspeed is now down to (55-30) = 25 mph. A ltr of fuel now takes me just (25/11) = 2.27 miles. If I push the throttle open a bit and raise the airspeed to 70 mph the groundspeed rises to 40 mph. A ltr of fuel takes me (40/15) = 2.67 miles at 70 mph. If I open the throttle a bit more and raise the airspeed to 85 mph the groundspeed rises to 55 mph and the ltr of fuel now takes me (55/20) = 2.75 miles. So when there is a good headwind you need to fly faster than the most economical still air airspeed for best economy. Now 85 mph is the best airspeed for fuel economy.
For a 10 mph headwind the figures for 55, 70, 85 mph are 4.1 miles per ltr, 4.0 and 3.7 so 55 mph is the best airspeed still.
For 20 mph headwind the figures are 3.2, 3.33 and 3.25 so 70 mph is the best economy airspeed.
Andrew.
These are real figures from a real aircraft.
Moderator
Fuel economy could be fuel consumption vs unit distance, or unit time.
If it is per unit time, you don't care where you are going (yes, could be hovering), and thus winds and groundspeed are not important. All you wanted was the longest time off earth, thus the least fuel burn per unit time, which will be achieved at an airspeed of best endurance. Any faster airspeed, and you're burning more fuel than you need to to simply stay aloft, any slower, and you're burning more fuel to overcome increasing induced drag. Winds and groundspeed don't have a place in those equasions that I can see.
If getting somewhere is entering the equasion, than it's an airspeed for best range, and that's fuel consumption per unit distance. Now wind and groundspeed play a vital role in the equasion...
Pilot DAR
If it is per unit time, you don't care where you are going (yes, could be hovering), and thus winds and groundspeed are not important. All you wanted was the longest time off earth, thus the least fuel burn per unit time, which will be achieved at an airspeed of best endurance. Any faster airspeed, and you're burning more fuel than you need to to simply stay aloft, any slower, and you're burning more fuel to overcome increasing induced drag. Winds and groundspeed don't have a place in those equasions that I can see.
If getting somewhere is entering the equasion, than it's an airspeed for best range, and that's fuel consumption per unit distance. Now wind and groundspeed play a vital role in the equasion...
Pilot DAR
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Winds and groundspeed don't have a place in those equasions that I can see.
But in the far majority of cases your best endurance speed will be higher than the windspeed so then it's not a factor indeed.
There are times when endurance is very useful eg holding although range is usually more of a consideration. I know I've used it on a number of occasions because of traffic, weather or the like ("There I was in the middle of the night over the North Sea in a gale waiting for FISO/ATC to get to my alternate so I could do the approach yada yada"). Sometimes the only way to carry sufficient fuel for the flight and still carry the payload is to plan holding at best endurance and alternates at best range speeds.
