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Maximum Range vs. Maximum Endurance


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One of my students approached me with this question today that I wasn't quite sure how to answer. Any thoughts are much appreciated:

 

"In an R22, if the maximum range is 83 KIAS, then why does Frank say in the safety video that the 'maximum endurance is 53 KIAS' when explaining the power curve?"

 

In other words, if you're trying to burn the least amount of fuel for the distance covered, should you pitch the nose for 53 KIAS or 83 KIAS?

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Exactly. Same thing with max distance in an auto. 70knts (or was it 75?) and 90% will let you glide the farthest. But 53knts will delay you hitting the ground for the longest.

 

 

We had a discussion about this once before. I think that 53 knots in an auto will be the slowest speed for the average pilot to have enough speed to flare. I think the slowest ROD in an auto would be just above ETL. In other words, the slowest speed at which you are flying away from your vortices. I think that any more speed will simply require a higher ROD. I have never tested this theory, but it makes sense in my head. Of course, there isn't much value in autorotating at just above ETL to save time, unless they are preparing your landing spot or something. Shortening distance is another matter.

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Example based on some rough numbers for the R22:

 

At 53 knots you can fly ~4 hrs at 7.5 gph..... 212 nm

 

At 83 knots you can fly ~3.5 hrs at 8.5 gph.... 292 nm

 

At 95 knots you can fly ~3.0 hrs at 10 gph.... 285 nm

 

So if you're trying to cover a long leg and fuel is tight, fly 83 knots. If you're doing some aerial work over a race, game, crime scene, etc fly 53 knots. If you're trying to get somewhere fast with plenty of fuel on board, fly at MCP.

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It all has to do with the power curve. In the R22, the bottom of the power curve is 53 knots. This is the speed for the lower power required. 206 is 60mph IIRC. You'll notice most aircraft are within about 10 or so knots of one another, mostly due to the way parasite drag increases exponentially.

 

So, whether you're in powered flight or non powered flight, the rotor will demand the least energy at 53 knots in the R22. Since in an autorotation you're getting the power to spin the rotor from your loss of altitude (excluding the flare), 53 knots is where you will have to use the least amount of altitude to maintain a set RPM.

 

As for the flare, is it wise to take 53 knots to the ground for an auto? Depends on your experience level. Frank recommends 60 knots minimum in the glide because you have a substantially larger amount of energy available in airspeed at 60 rather than 53 knots. Remember, airspeed is exponential. I want to say it's almost twice as much energy to use, but it's been a while since I looked at the numbers.

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The difference between the flare at say 50 and 60 is pretty huge. I have students do it at both so they can see why they need to keep at least 60, but if they mess up they can know what to expect if they're on their own.

 

53 - max endurance speed will keep you in the air the longest amount of time.

This is due to the least amount of total drag meaning less power required to fly. (as stated before this can be engine power or aerodynamic power in an auto)

 

 

83 - max range speed will get you the farthest distance but you'll be in the air a little shorter.

You just get farther when you go faster.

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RockyMountainPilot said:

 

I think that 53 knots in an auto will be the slowest speed for the average pilot to have enough speed to flare. I think the slowest ROD in an auto would be just above ETL. In other words, the slowest speed at which you are flying away from your vortices. I think that any more speed will simply require a higher ROD. I have never tested this theory, but it makes sense in my head. Of course, there isn't much value in autorotating at just above ETL to save time, unless they are preparing your landing spot or something. Shortening distance is another matter.

 

There is at least one point in this message I feel is incorrect. The point is, "the slowest ROD in an auto would be just above ETL."

 

It is my understanding that 53kts gives the slowest rate of descent in an autorotation, not an airspeed just above ETL. Below 53kts the total drag increases with the increase in induced drag as airspeed slows. An airspeed just above ETL will result in a higher rate of descent than 53kts.

 

-Cheers

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You can picture your approaches. As you near ETL (still above) you already bringing in power to control the descent rate. The farther you get from 53kts (in an R22) the more drag you have. Below 53 it's the induced drag increasing and above it the parasite drag increasing.

 

Something that's not in the 22 poh but was mentioned at the safety course is that the min. descent configuration for an auto is 53kt @ 90% rpm. You just kind of float there. Next time you're with your instructor doing autos check it out. Just get the rpm to 97% before 500agl to be safe.

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  • 1 month later...

Ok, so the best endurance speed comes from the lowest point on the Total Drag Curve, and coincides with the best rate of climb(or Vy if you wanna get all airplaney) and minimum rate of decent in an autorotation.

 

The Maximum Range speed(or Vmr) works slightly different. Some people use the Power required/TAS curve for this like Phil Croucher in his JAA books and "the helicopter pilots handbook". And some people use the Fuel Flow/TAS curve like Shawn Coyle in "Cyclic & Collective"(pages 247 & 249). Both graphs are pretty intimately related so I guess "it's six of one and a half dozen of the other" as my Mom always says!!

 

The figure of 83kts as best range speed in a R22, I believe is got from drawing a Tangential line from the the Fuel Flow/TAS curve to the origin, which in a no wind condition would be the 0kts point. The point where the tangent touches the curve is your Vmr speed.

 

Now in a head-wind condition, your origin is no longer the Zero Knots point along the bottom of the graph. So, if you want to find out Vmr for 25kts head-wind condition your origin would be the 25kts point on the bottom of the graph. In this case the tangent would touch the curve at higher True Airspeed, and that would then be your Vmr for that 25kts head-wind condition.

 

For a tail-wind condition you will find your origin by moving to the left side of the 0kts point on the graph and draw the same speed scale on the other(blank) side along the bottom of the graph, starting at Zero and increasing the numbers as you move left(and maybe put a minus symbol beside them to indicate tail-wind). If you have a 30kts tail-wind, you would draw the tangent line from the -30kts point on the graph tangential to the Fuel Flow/TAS curve. Where it touches the curve is now your Vmr for that tail-wind condition.

 

So for a head-wind you will have a slightly higher True Airspeed as your Vmr, and a lesser one for a tail-wind. Also, looking at the shape of the Fuel Flow/TAS or Power Required/TAS curves, I'm guessing that a particular amount of tail-wind would have a greater impact on Vmr than the same amount of head-wind. The changes in Vmr are quite small in comparison to the changes in tail-wind and head-wind components that affect them, especially the type of winds that most Robinson pilots venture out in. Which is probably why the Frank has just set 83kts as the figure. Pilots venturing out in larger ships in North-Sea conditions or some GOM conditions may pay more attention to these changes.

 

Now, could someone set me straight on which graph is the best one to use for this? I'm guessing the Fuel Flow/TAS graph as at the end of it all this all boils down to making the most of your fuel.

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The airspeed for maximum range with a 25 knot headwind (or tailwind) is going to be 83 KIAS. What the maximum range is will be determined by groundspeed. I think Frank (his test pilots, actually) determined the Vmr by test flight when they were plotting the performance graphs for the R-22.

 

I believe Vmr is going to be largely based on aerodynamics - your best fuel burn for a specific weigh will be at a given airspeed. That fuel burn gets better as weight decreases, but in an R-22 you really don't carry that much fuel. In a larger turbine you may monitor fuel flow and quantity to determine how much time you have remaining under the current conditions, but I don't think you would use it to say "Hmm, I should speed up to 120 knots to get better range."

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In a larger turbine you may monitor fuel flow and quantity to determine how much time you have remaining under the current conditions, but I don't think you would use it to say "Hmm, I should speed up to 120 knots to get better range."

 

Ok, so obviously you wouldn't use this method on the fly, but it is a useful thing to know if venturing out in strong winds.

 

What the maximum range is will be determined by groundspeed.

 

So are you saying that my understanding of this concept is flawed? I'm not challenging you. I just want to get the theory right and having read the material on this in those books, this is how I understood it worked. Do you know the part of "Cyclic & Collective" I'm talking about?

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No, I don't have Cyclic and Collective, so I'm not sure about the graph you're referencing. I can understand using a fuel flow vs. TAS curve to maximize endurance, but I'm not making the connection to wind direction and speed that you're bringing up. True Airspeed is just Calibrated Airspeed corrected for density altitude, right? So if you're flying 120 knots TAS with a 25 knot tailwind you will have a 145 knot ground speed, with the same amount of headwind you will have a 95 knot groundspeed. Obviously this will have a major effect on your range, but the wind has no effect on your burn rate since the helicopter sees itself at 120 knots TAS regardless. Or am I missing the point entirely?

 

To step back to the R-22 world, I don't think density altitude is much of a factor with the R-22 since we run full rich all the time. That may be why there is a fixed airspeed for best range. I know with turbines the fuel numbers get better with altitude and that may be where the reference to TAS enters things.

 

Also, for the record, I am by no means an authority - I'm exploring these questions with you... :-)

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Alright, so I spoke to someone with a much better understanding of this subject than me and he confirmed that what I had written above is correct. I was thinking about it a little more and I thought a good way to explain increasing Vmr for a headwind would be this;

 

So take your Vmr of 83kts while flying a R22 and, then say you encounter a headwind of 83kts(extreme, I know. But just roll with it). So you're flying at 83kts TAS but your ground speed is now 0kts. If you increase your speed to 93kts you now fly 10 nautical miles in 1 hour where you would have only been stationary over the ground at 83kts. So therefor in that example, you get better range by increasing your TAS in a head-wind condition.

 

With an increasing tail-wind, the Vmr will keep decreasing until you reach Vy(or slightly above it, as the tangent line will never touch the curve directly at the bottom) which is our best endurance speed as it is at the bottom of the power required or total drag curves.

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Glider pilots use the drag curve and work out best speed to fly the same way you show depending on head/tail winds. As far as I can tell it works on just about anything that flys but a balloon or paraglider.

 

Jerry

 

 

Ok, so the best endurance speed comes from the lowest point on the Total Drag Curve, and coincides with the best rate of climb(or Vy if you wanna get all airplaney) and minimum rate of decent in an autorotation.

 

The Maximum Range speed(or Vmr) works slightly different. Some people use the Power required/TAS curve for this like Phil Croucher in his JAA books and "the helicopter pilots handbook". And some people use the Fuel Flow/TAS curve like Shawn Coyle in "Cyclic & Collective"(pages 247 & 249). Both graphs are pretty intimately related so I guess "it's six of one and a half dozen of the other" as my Mom always says!!

 

The figure of 83kts as best range speed in a R22, I believe is got from drawing a Tangential line from the the Fuel Flow/TAS curve to the origin, which in a no wind condition would be the 0kts point. The point where the tangent touches the curve is your Vmr speed.

 

Now in a head-wind condition, your origin is no longer the Zero Knots point along the bottom of the graph. So, if you want to find out Vmr for 25kts head-wind condition your origin would be the 25kts point on the bottom of the graph. In this case the tangent would touch the curve at higher True Airspeed, and that would then be your Vmr for that 25kts head-wind condition.

 

For a tail-wind condition you will find your origin by moving to the left side of the 0kts point on the graph and draw the same speed scale on the other(blank) side along the bottom of the graph, starting at Zero and increasing the numbers as you move left(and maybe put a minus symbol beside them to indicate tail-wind). If you have a 30kts tail-wind, you would draw the tangent line from the -30kts point on the graph tangential to the Fuel Flow/TAS curve. Where it touches the curve is now your Vmr for that tail-wind condition.

 

So for a head-wind you will have a slightly higher True Airspeed as your Vmr, and a lesser one for a tail-wind. Also, looking at the shape of the Fuel Flow/TAS or Power Required/TAS curves, I'm guessing that a particular amount of tail-wind would have a greater impact on Vmr than the same amount of head-wind. The changes in Vmr are quite small in comparison to the changes in tail-wind and head-wind components that affect them, especially the type of winds that most Robinson pilots venture out in. Which is probably why the Frank has just set 83kts as the figure. Pilots venturing out in larger ships in North-Sea conditions or some GOM conditions may pay more attention to these changes.

 

Now, could someone set me straight on which graph is the best one to use for this? I'm guessing the Fuel Flow/TAS graph as at the end of it all this all boils down to making the most of your fuel.

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  • 6 months later...

Found this thread looking for something else on Google.

 

It's a good topic and worth bringing up again.

 

With the engine off (or at idle), at a constant rotor rpm and pitch setting, in a steady state autorotation, the rotor produces only so much lift (according to the math). The minimum rate of descent airspeed correlates to the lowest point on a total drag chart. In essence, it is where the rotor has to work the least to provide lift/thrust for the aircraft. Starting at the minimum rate of descent airspeed, the rate of descent increases as you both speed up and slow down. Going slower than minimum rate of descent airspeed allows a more vertical flow of air (inflow or upflow) through the rotor, which results in a similar effect to increased induced flow and is essentially a less efficient extraction of energy from the upward flow of air. Going faster than minimum rate of descent airspeed increases the parasitic drag of the airframe and profile drag of the rotor.

Edited by Linc
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Man, I must've been tired. I latched onto a tangent and totally missed the context of this conversation.

 

First time that's ever happened! (rolls eyes)

 

Anyways, to add to my tangent. After thinking about it some more, I'm reminded that there can be a difference between max endurance/max climb airspeed and minimum rate of descent airspeed. For my helicopter, it can be 5-10 knots. Our maintenance test pilots conduct checks to ensure that the blades are mechanically set to provide 100% rotor rpm (in the green) at the aircraft's listed minimum rate of descent airspeed. This is done periodically because the optimum setting changes with the temperature and altitude. Somehow, this is also a design airspeed, not necessarily a purely aerodynamic one.

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Linc,

 

Another very plausible reason is the calibration of the pitot tube. In the A119 there can be up to a 17kt error in autorotation compared to level flight. 65kts is the average VY, but Least rate of decent is 80kts. Compare it with the GS off of a GPS and you can easily see the error. Add to that the parasite drag difference on the fuselage in climb compared to decent and you may find another culprit for dissimilar climb/decent speeds. Most civilian aircraft don’t have performance charts for fuel flow, but max range and max endurance are affected by temp and altitude as well. Just to throw a little mud on the equation...

Edited by C of G
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I'm also thinking that it might have to do with the weight of my aircraft, which often takes off at or close enough to MGW that it might as well be. The RFH says in Chapter 11, "When the helicopter is operated with heavy loads in high density altitude or gusty wind conditions, best

performance is achieved from a slightly increased airspeed in the descent."

 

It reminds me that those checks the maintenance pilots do are calculated for a certain weight, a weight that is closer to almost empty fuel levels. Even then, minimum rate of descent for my aircraft slows my descent over a different airspeed slightly less than the air resistance of a falling rock. So all of this is simply academic discussion. :D

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  • 5 years later...

Darren - The fuel flow is used for turbiine helicopters.

 

On a turbojet (airplane), each pound of drag needs a pound of thrust to maintain level flight, which is directly proportional to fuel flow, so range and performance can be checked with a total drag curve. In a helicopter, thrust production is not directly related to fuel flow, so you can’t use a total drag curve in the same way.

Power required curves are really fuel flow curves.

 

How are you getting on anyway? :)

 

Phil

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