Drag Charts v. Cruise Charts (Relating to Max Endurance and Max Range)

[cts484]

I am looking for an explanation of Drag Charts and Cruise Charts (aka Power Curves).  I am an Army Aviator and the majority of my questions are coming from TC 3-04.4: Aerodynamics of Flight (Pgs 1-27, 1-28).

1-78. Maximum range airspeed is an airspeed that should allow the helicopter to fly the furthest distance. It is determined by flying where airspeed intersects the lowest amount of total drag (point E on figure 1-41, page 1-27). However, due to flight testing and aircraft performance, cruise charts are used to determine torque and fuel flows required to maintain that airspeed. Because cruise charts are not drag charts, it can be noted the lowest point of a drag chart does not necessarily match the lowest point of the power required curve in a cruise chart.

1-79. Maximum Endurance airspeed is an airspeed that allows the helicopter to remain flying the most amount of time. It can be found on the power required curve of the cruise chart where power required is at its lowest and not necessarily where total drag is lowest on the drag chart.

 

Questions:

-Why isnt Max Endurance ALWAYS the lowest total drag?  What factors make it not the least amount of drag?

-What factor(s) make drag charts different from cruise charts/power curves?

 

[Eric Hunt]

I don't know why your books have separated the drag and the power.

 

Normally, those curves would be called "Power required to overcome..profile drag / induced drag / parasite drag", and when combined, the axes of the chart would stay the same - but your book has twisted the next chart, the "total drag curve", around to put speed on the y axis, and left off the data between 0 and 60 kt. It is far easier to understand if it is on the x axis, like on the first  "drag" chart. The Total Drag curve should be the same orientation as the curve "D-E Total drag" on the first chart. It won't be the same curve, because the drag is factored by the speed to get power, but the shape will be similar - see that they show that max endurance isn't at the apex on the drag chart, but it is on the power chart.

Then it will be easier to see that the bottom of the power curve is where power required is least, (near point E on the drag curve), so it is the best endurance speed. It is also going to be very close to the best climb speed, if the "Power available" curve is also laid over the chart. When the gap between power available and power required is at its maximum, you have the most excess power to use for climbing.

For range, it is a line drawn from the origin to be the tangent to the curve. The line is close to the curve over a spread of speeds, so it might be more convenient, for some other reason, for the manufacturer to nominate a speed that isn't at the exact tangent point.

Rotating those second and third curves doesn't appear to make any sense. 

(Waiting now for Helonorth to make his usual attack on me. Come on, you know you want to...)

[cts484]

Eric, thanks for taking the time to respond to my questions.

Can you explain more what you mean by "It won't be the same curve, because the drag is factored by the speed to get power, but the shape will be similar - see that they show that max endurance isn't at the apex on the drag chart, but it is on the power chart."

Why are the curves not the same (Why are the apexes different?  Why isnt power directly related to total drag?  As I increase in airspeed the power required will decrease past TFE and ETL because induced drag decreases.  As I continue to increase airspeed, eventually parasite drag will drastically increase requiring more power.  I recognize that I am probably oversimplifying things but I am trying to figure out what factors make the apexes different.

[Eric Hunt]

Because in its simplest form, Drag x Speed = Power. And drag is proportional to Speed squared, so power is proportional to Speed cubed. That's why the apex moves up the curve. Similar shapes, but the apex is not in the same place.

Edited August 2, 2020 by Eric Hunt

[V-any]

I look forward to being told that I'm wrong, and how, but to me that chart doesn't make sense.

An aircraft in a steady state is in balance. It's losing energy continuously due to drag. The aircraft has to make power to replace that energy to keep it in a steady state. Therefore, minimum total drag should be the point where the least power is required.

So, by my understanding, max endurance should be somewhere near minimum total drag, aka least power required.

The only caveat I can think of is that power produced at the rotor blades might not necessary scale linearly with fuel flow, and ultimately, it's fuel flow that we're concerned with; it's a factor in both performance measures. Max range is knots/fuel-flow. Max endurance is simply the speed where fuel-flow is the least. If you want to find max endurance, go to to your cruise charts and find the cruise configuration where your fuel flow is the least.

Edited August 3, 2020 by V-any

[Eric Hunt]

This chart is from your FAA -H-8083-21B handbook. 

Note that it talks about Power, not Drag. Yes I can see why you are hung up on drag, but it is the Power Required to Overcome Drag that is why you stay in the air - or not. Multiply drag times speed to get the basis of power.

And as usual, this book is full of errors. It labels the right side of the rising curve as "power required to hover OGE", but the corresponding speeds range from 65kt to 100kt. That caption should be at the far left, at 0 kt. 

Edited August 3, 2020 by Eric Hunt

[V-any]

21 hours ago, Eric Hunt said:

Multiply drag times speed to get the basis of power.

Why?

[Eric Hunt]

V-any, are you looking for the definition of Power?

Or are you asking why there are 2 charts, one showing drag and the next showing power? The power chart is a slightly different shape from the drag chart, because speed has to be factored in. You won't overcome any drag without using power.

Work = Force x distance, the force in this case is Drag, proportional to Speed squared (CL x 1/2 rho x speed squared)

Power = work / time

So, Power = drag(speed squared) x distance / time, and distance / time = speed, which makes the equation:

Power = speed cubed times the Bernouilli bits. Simples.

Edited August 5, 2020 by Eric Hunt

[V-any]

On 8/4/2020 at 1:12 AM, Eric Hunt said:

Power = speed cubed times the Bernouilli bits

So how much power is required when you're in a hover (speed is zero)?

[Eric Hunt]

The power curve is made up of 3 components, one of which is the power to overcome induced drag, which is greatest at zero airspeed. It then works its way down. Of the other 2 components, one starts at either zero and the other is at a mid-level, and work their way up.

The induced flow is moving, it still takes power to suck the air from the top and push it out the bottom. And power to overcome transmission drag, hydraulic pumps, generators and such.

But I know you were just having a poke for fun. Too easy.

 

Edited August 7, 2020 by Eric Hunt

[V-any]

On 8/7/2020 at 1:20 AM, Eric Hunt said:

But I know you were just having a poke for fun. Too easy.

Lol, was just an easy example.

I'm always interesting in learning, so I'm going to explain this the way I understand it in hopes that you either concur, or can explain why I'm wrong. However, I can say without hesitation that if this was as simple as the power required chart being the total drag chart multiplied by speed, then the power required would trend towards zero at zero airspeed, which it obviously doesn't.

In the case of helicopters, we're turning a shaft, not thrusting the aircraft (within linear thrust like a jet engine). In a helicopter, the engine power isn't thrust multiplied by speed, it's torque multiplied by RPM.

We can assume that RPM (N2) is constant, so that makes torque linearly proportional to horsepower. This means that regardless of flight condition, at any given torque, the engine is producing the same amount of horsepower (work) and burning the same amount of gas. The engine is producing the same amount of power hovering at 80%Tq as it is flying 100kts and pulling 80%Tq.

So, power available is torque available (multiplied by some constant). Thus, the point at which you require the least amount of power should be the point at which you have the lowest amount of total drag.

As long as fuel burn is linear with torque, maximum endurance speed will be the lowest torque setting, which should be the lowest point on the total drag chart.

---

As an aside, there are a few things that I think often obfuscate this topic:

One is that you could be talking about the power produced by the engine specifically (which is more natural from a pilot perspective, because we have engine gauges) OR you could be talking about the power produced by the entire power train and aerodynamic surfaces.

The second factor is that the engine is a turboshaft. This is different than a turbojet or rocket engine, where thrust available is linear and relatively constant and power increases as speed increases (due to multiplying by speed).

The third is that the rotor system directly produces both lift and thrust, not primarily thrust like in an airplane. So, at a hover, the system in it's entirety isn't producing any work (because the helicopter isn't moving). However, it is producing an upward force equivalent to its weight, and the engine is producing power in the form of turning the drive shaft.

 

Edited August 9, 2020 by V-any

[Eric Hunt]

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However, I can say without hesitation that if this was as simple as the power required chart being the total drag chart multiplied by speed, then the power required would trend towards zero at zero airspeed, which it obviously doesn't.

Remember that the "speed" can be the physical speed of the aircraft through the air (parasite and profile drag increasing) or it can be the Relative Air Flow (RAF) to the blades in the hover or in forward flight. (Induced Flow).  In the hover, the downward induced flow is highest, and the Total Reaction is tilted further back from the RAF. It is producing plenty of lift, but a larger component of it is pointed backwards (drag) and the drag component points downwards (weight), so the poor old rotor is producing Lift+Thrust to overcome it. The speed squared is the RAF, in this case, and is certainly not zero when in the hover. In forward flight, there is less IF, so the TR moves forward, more is available for Lift and less is used up in Drag, so the curve moves downward while the others move upward.

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So, at a hover, the system in it's entirety isn't producing any work (because the helicopter isn't moving).

The work being done is pushing the airflow downwards. No work, no fly.

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 power produced by the entire power train and aerodynamic surfaces.

The engine is the ONLY thing producing power, the rest of them are chewing it up. The power can be converted to Kinetic Energy (speed) or Potential Energy (altitude) and these are the things that you can use up to produce the autorotative forces that allow you to control descent when the engine goes on holidays. But you only get one bite at KE+PE, once you use it, it's gone.

 

[iChris]

On 8/1/2020 at 4:32 PM, cts484 said:

Because cruise charts are not drag charts, it can be noted the lowest point of a drag chart does not necessarily match the lowest point of the power required curve in a cruise chart.

1-79. Maximum Endurance airspeed is an airspeed that allows the helicopter to remain flying the most amount of time. It can be found on the power required curve of the cruise chart where power required is at its lowest and not necessarily where total drag is lowest on the drag chart.

Questions:

-Why isnt Max Endurance ALWAYS the lowest total drag?  What factors make it not the least amount of drag?

-What factor(s) make drag charts different from cruise charts/power curves?

 

The text you quoted states that "cruise-charts are not drag-charts, it can be noted the lowest point of a drag chart does not necessarily match the lowest point of the power required curve in a cruise chart."   

 As in Eric Hunt's post above, D = P/V. Were P = rotor power (induced, profile) + the rest of the helicopter (parasitic, tail rotor).

 Eric already answered your question as to why. It's in the math, rearranging the equation D x V = P. It's a helicopter, not just D = P. You  have to account for the V and the other power requirements.

 We're dealing with the total power required supporting more than just the drag of the helicopter. The issue is forward flight (cruising flight) performance. Another power drain is that the turbine engine is more efficient at high power than at low power because of the fuel-flow needed to keep the gas generator spinning, regardless of the power output. Fuel-flow is the center of interest. Remember, fuel-flow is proportional to power; that's why fuel-flow versus airspeed curves mimic the power-required curves. Power is proportional to Fuel-flow.

 To maximize endurance, we want to maximize the amount of time that we can stay in the air. Since the fuel flow is proportional to the power-required, fuel flows lowest when the power-required is a minimum. The speed corresponding to the bottom of the power-required curve is the speed for maximum endurance.

 To maximize the range, we want to get the maximum distance for each pound of fuel burned. Therefore, the maximum range airspeed occurs where a line from the origin is tangent to the power required curve or fuel-flow versus airspeed curve below.

Edited August 16, 2020 by iChris

[cts484]

Thank you all for taking the time to provide your input and insights.  All of your explanations helped me understand the charts a lot better.  Thanks for a good discussion!

[Loic]

On a different approach:

Maximum range is a result of distance.

Maximum endurance is a result of time.

So we are really trying to discuss if the maximum of "miles/gallon" happens at the same time as the maximum of "hours/gallon".

Taking example:

If my maximum range (=minimum drag) is at 105 knots, let say for the sake of the example I have 30 gallons of fuel that burns in 3 hours giving me a range of 315 miles - 3 hours flight - 10 gallons/hour

 

So if the speed decrease by 10%, assuming drag increase by 5% (we know it is not linear) but now I don't need to pull so much collective to maintain my forward speed, so I need less power and say my gas consumption actually decrease by 5% (more drag to fight but less forward trust to generate):

I am now traveling at 94.5 knots (105 - 10%), but gas consumption is now 9.95 gallons/hours so with 30 gallons I have 3.015 hours of flight - 285 miles range...

So I fly longer period of time, but since I am slower I don't travel so much.

 

Real question becomes why do we have to pull less collective while traveling at slower speed as it is counter-intuitive with what the drag curve says... But I believe this is due to the direction of trust:

The vertical component of the trust must remain equal to the weight to maintain altitude, but at slower speed I need less horizontal trust so overall total trust required is less at slower speed than higher speed (really? lol) --> so less collective, so less power required (as long as ETL is maintained).

Comes down to comparing the evolution of forward trust versus the drag. And both of those are obviously not linearly corelated.

 

So above ETL:

The slowest we are, the less forward trust we need, so the less collective we need, so less power required, so more endurance.

The slowest we are (between max range speed and ETL), the more drag (due to induced drag) we fight, so the more power we need, so the less endurance. 

Both phenomenon are fighting each other ==> The inflection point (maximum endurance) being when the drag starts to increase at a faster pace than the trust decrease.

[HEMSLAWS]

Military aircraft can have massive changes in drag(s) based upon their configuration/loading. The cruise chart section of the -10 should have a method of factoring in your particular drag configuration into the speed and or fuel burn effects for various altitude/temp conditions.