Figuring out Carson’s speed.

[A64Pilot]

16 hours ago, Will.iam said:

Might be true of a fishing boat but a ski boat definitely once on up on a plane and be throttled back a few 100 RPM’s and still stay on the plane and that’s your best cruise speed on my boat anyway. Better if there is a slight ripple in the water, glass smooth is actually more drag and half ft waves or bigger is too rough to stabilize at that reduced throttle so very specific weather conditions in order to achieve the results 

You know I would have bet money on that too, you can feel the boat speed up just as she breaks onto plane and once your over that hump you can back off a little and stay there, everybody knows just on plane is the most efficient speed. oh and trim tabs help.

But I had the same results on our little dive boat, a 21’ CC with a 175 HP Mercury Verado. Sometimes things your sure of break down when actually tested, you have to have instrumentation though, on the dive boat it was easy, the Garmin Radar / Plotter was connected to the Verado’s Can Bus and gave instaneous MPG.

On edit if graphed speed on the bottom and fuel on the side, it gets very steep climbing onto plane, but there was no steep decline just after it broke onto plane, rather the curve flattened out, then as speed increased began to rise again. If only max range was the issue and time not considered, best MPG was at idle, by a surprising amount, but who can idle around to travel.

To continue this on a boat anyway fuel consumption vs speed began to climb the moment you started to have a wake, which makes sense because the energy to roll that wake of course comes from your gas tank. When we were cruising that was something that the Trawler guys didn’t like to hear. Now for most engines there is a “magic” RPM, that is one RPM where the BSFC is greatest, but the drag cost of increased speed overcomes it.

For example there are a great many people that are convinced their car gets better fuel mileage at say 70 mph than any lower speed, but that’s not the case unfortunately. The 55 MPH speed limit did work, but it drove me nuts.

On edit, if you have ever flow a float airplane you plow along at full throttle until it gets on step, then once on step it will accelerate quickly and fly, but if your heavy getting on step seems to take forever, obviously there is a decrease in drag once it gets on step, but it still takes quite a bit of power to stay there, so intuitively it seems obvious that step taxiing is much more efficient than being off the step, but for some reason the numbers show it’s not. I haven’t tested an airplane, but use it as an example because, well this is an airplane forum.

 

[Shadrach]

On 4/16/2023 at 3:22 PM, A64Pilot said:

No, Vy is one exact speed that can be duplicated by test flight, one kt faster or slower and the climb rate will be less.

Carson’s speed as I understand it is an arbitrarily picked point, it’s not for example the speed at which the highest mpg is attained.

Hint, what Carson was trying to quantify will be a different formula for different airframes, but as a “rule of thumb” it’s fine. It’s close enough, and the concept of close enough is important, the differences will be tough to measure.

But to think you need to multiply best glide by exactly 1.32 and come up with one exact airspeed is not nearly as important as some will make it seem.

It’s really just like an automobile, if you want to increase fuel milage, slow down. Just like an automobile there is a speed at which if you go slower fuel milage will go down, but it at such a ridiculously low speed, who’s going to drive or fly like that? So slow down some, not so much you’re going nuts or the airplane flies like a pig. Remember the 55 MPH speed limit on Interstate highways? Drove me nuts.

For my J who’s best glide at max gross is 90 kts I think, 1.32 x 90 = 118.8 kts, actually a little less as most of us aren’t at max gross in cruise.

I’ve flown at 120 kts quite a bit, and on cooler days in Fl, I can’t get my cyl head temp high enough if I’m LOP, so it’s not a viable cruise speed, middle of a Fl Summer it’s OK, but to me it flies like a dog, so I ended up bumping it to 130 ish kts at 8 GPH and the fuel burn difference over my normal go out to eat flights is something like 1/2 gl more and the airplane flies better and my temps are in the middle of the green

Carson speed is simply a measure of highest velocity per unit of input. In contrast to longest distance covered per unit of input. One is no more arbitrary than the other.  Also, it’s a drag calculation, incorporating mixture setting just muddies the concept. If Carson speed is attained at 50% power, it requires 50% power. I does not matter if you’re rich or lean of peak, 50% power is the required power setting. The most efficient setting that yields the required 50% power is a different discussion.

[Andy95W]

I know the Carson speed for my airplane, and I’m glad for it.  I figure there are 3 good speeds to know for your airplane: full-tilt, where you go fast but burn an idiotic amount of fuel; best range, where you are most efficient but go an idiotically slow speed; and Carson’s speed, which is basically the least idiotic speed to fly.

With all that said, I cannot remember a single flight where I intentionally flew Carson’s speed.  There have been a couple of flights around 11-12,000 feet where I happened to glance at the airspeed and noted I happened to be at my Carson speed.  I’ll admit it was very rewarding basking in the warm glow knowing I was perhaps slightly less of an idiot those times.

[AH-1 Cobra Pilot]

1 hour ago, Shadrach said:

Carson speed is simply a measure of highest velocity per unit of input.

Absolutely not!  What you are describing is a curve, not a point/speed.  Carson chose a point on that curve at which a line was tangent, but the slope of that line is utterly arbitrary.  (In his paper, he does what is commonly referred to a "hand-waving" to justify the slope.)  As I have said before, you need one more equation, because you have one too many variables to come up with an optimal 'speed'.

[jaylw314]

42 minutes ago, AH-1 Cobra Pilot said:

Absolutely not!  What you are describing is a curve, not a point/speed.  Carson chose a point on that curve at which a line was tangent, but the slope of that line is utterly arbitrary.  (In his paper, he does what is commonly referred to a "hand-waving" to justify the slope.)  As I have said before, you need one more equation, because you have one too many variables to come up with an optimal 'speed'.

Calling it 'hand-waving' or arbitrary does not make it so.  I suspect you are looking at the graph of D/L vs V  (Fig 2) in isolation.  The slope of that line is mathematically derived previously from the lift/drag equations as the minimum of E/s (fuel flow) / velocity, and then he goes on to talk about the empiric observations by von Karmann that seem to support this theoretical conclusion.

Again, whether fuel flow per unit velocity is an important measure to you or not is up for you to decide, and I think it's sort of useful but not something I want to minimax all the time.

[AH-1 Cobra Pilot]

3 hours ago, jaylw314 said:

Calling it 'hand-waving' or arbitrary does not make it so.  I suspect you are looking at the graph of D/L vs V  (Fig 2) in isolation.  The slope of that line is mathematically derived previously from the lift/drag equations as the minimum of E/s (fuel flow) / velocity, and then he goes on to talk about the empiric observations by von Karmann that seem to support this theoretical conclusion.

Again, whether fuel flow per unit velocity is an important measure to you or not is up for you to decide, and I think it's sort of useful but not something I want to minimax all the time.

Okay, maybe I missed something.  What is the slope of that line?

[jaylw314]

3 hours ago, AH-1 Cobra Pilot said:

Okay, maybe I missed something.  What is the slope of that line?

I misspoke, the slope is an ideal, not arbitrary value (probably the wrong terms).  He's trying to show that maximizing power per unit velocity was what von Karmann was actually interested in as his measure of 'efficiency,' as mapped out in his space of P/V vs V.  It's not relevant to the calculation of Carson's speed, he's showing an empiric example of someone else who was interested in the maximum value of dP/dV when talking about efficiency.

He had already mathematically calculated the maximum of value of dP/dV at the bottom of page 3.

[AH-1 Cobra Pilot]

15 hours ago, jaylw314 said:

I misspoke, the slope is an ideal, not arbitrary value (probably the wrong terms).  He's trying to show that maximizing power per unit velocity was what von Karmann was actually interested in as his measure of 'efficiency,' as mapped out in his space of P/V vs V.  It's not relevant to the calculation of Carson's speed, he's showing an empiric example of someone else who was interested in the maximum value of dP/dV when talking about efficiency.

He had already mathematically calculated the maximum of value of dP/dV at the bottom of page 3.

I see this:  "This quantity has a minimum, i.e., ... when a* = 3^1/4, but I do not see the other.  What is the maximum of value of dP/dV?

On the next page:  "This result is remarkable on two counts: first, it indicates that the common practice of operating piston aircraft at airspeeds about 30% higher than the optimum has a rational basis, although the practice itself has probably evolved empirically." 

On previous posts, it is noted that this is absolutely not true for Mooneys.  That kind of destroys his whole thesis, does it not?

When you have fewer equations for your number of variables, your answer is a curve.  The only way to get a point-solution is to add another equation to the solution.  One way to do that is to insert your own determination of the cost of your time.  i.e. If you take fuel at $5/gallon and your time at $100/hour, I guarantee you will be able to determine the exact airspeed to fly.  Ahh, but, you say, my time is worth $110/hour!  So, some might even consider that solution arbitrary.

[jaylw314]

1 hour ago, AH-1 Cobra Pilot said:

I see this:  "This quantity has a minimum, i.e., ... when a* = 3^1/4, but I do not see the other.  What is the maximum of value of dP/dV?

Sorry, that should be minimum, not maximum, I keep confusing myself about that.  He showed that fuel flow is proportional to power, and uses the term omega to refer to fuel flow and alpha to refer to airspeed, then sets the derivative of omega/alpha to zero to find the minimum.  He does it in a weird way to remove units, but that kind of obfuscates the actual conclusion, so I'm not sure why he does it that way.

1 hour ago, AH-1 Cobra Pilot said:

On previous posts, it is noted that this is absolutely not true for Mooneys.  That kind of destroys his whole thesis, does it not?

I don't remember that, I recall people have discussed that best glide is sometimes higher than both Vx and Vy, but since Vx and Vy are partly determined by max engine power, they're not relevant to his discussion (equilibrium at cruise).

1 hour ago, AH-1 Cobra Pilot said:

When you have fewer equations for your number of variables, your answer is a curve.  The only way to get a point-solution is to add another equation to the solution.  One way to do that is to insert your own determination of the cost of your time.  i.e. If you take fuel at $5/gallon and your time at $100/hour, I guarantee you will be able to determine the exact airspeed to fly.  Ahh, but, you say, my time is worth $110/hour!  So, some might even consider that solution arbitrary.

This is absolutely incorrect.  When you have only a straight line, picking a point is arbitrary without another line.  When you have a curve, you have plenty of unique points--local minima/maxima, absolute minimum/maximum, points of inflection, and whatnot--without requiring another line or curve.  That's not to say your personal preferences don't matter to how you decide to do things, but physics (and math) doesn't give a rat's ass about your preferences.  It just gives you information that applies to everyone regardless of preference, then you can decide otherwise.

Edited May 2, 2023 by jaylw314

[AH-1 Cobra Pilot]

1 hour ago, jaylw314 said:

This is absolutely incorrect.  When you have only a straight line, picking a point is arbitrary without another line.  When you have a curve, you have plenty of unique points--local minima/maxima, absolute minimum/maximum, points of inflection, and whatnot--without requiring another line or curve.  That's not to say your personal preferences don't matter to how you decide to do things, but physics (and math) doesn't give a rat's ass about your preferences.  It just gives you information that applies to everyone regardless of preference, then you can decide otherwise.

IF that is incorrect, you prove it.  Graph y=x² for x=1 - 10, which is a similar curve in the chart Carson uses.  Tell me where the optimum point is. 

He does it by using his "Limit Line", (or in other words, adds another equation), which comes from a paper by other authors that may or may not be relevant, then justifies his choice thus, "Their work showed that there is an apparent technology barrier (which they cautiously referred to as "almost a kind of universal law")..."  If that is not hand-waving, I do not know what could be.

[Andy95W]

[jaylw314]

34 minutes ago, AH-1 Cobra Pilot said:

IF that is incorrect, you prove it.  Graph y=x² for x=1 - 10, which is a similar curve in the chart Carson uses.  Tell me where the optimum point is. 

Sorry bud, you were the one making extraordinary claims so the burden of proof is on you.

[carusoam]

Where is our Carson Speed Guru?  We sorta have one…  he wrote a master’s thesis on the topic.

let’s invite @testwest to the conversation…

Carson’s speed is the speed you use when ATC sends you in a direction you don’t want to go…

This can happen when flying IFR… and they can’t work you into the system…. They give you a heading 180° away from where you want to go…

No need to fly Mooney speeds to go the wrong direction… 

There is one Mooniac that flew across the country on one tank of gas… efficiency was everything for that trip.

@201er has done some pretty long flights into sparsely populated areas… where fuel economy can become important…

Best regards,

-a-

[Andy95W]

5 hours ago, carusoam said:

 

Carson’s speed is the speed you use when ATC sends you in a direction you don’t want to go…

Best summation of Carson’s speed I’ve read.

[Shadrach]

30 minutes ago, Andy95W said:

Best summation of Carson’s speed I’ve read.

@carusoam @Andy95W

Why would you use Carson speed when flying opposite the desired direction of flight? Why not just slow to L/Dmax at that point?

[Andy95W]

For the times ATC needs to give vectors in order to maintain lateral IFR separation requirements.

If they give a holding pattern to gain time separation, then L/Dmax.

[Andy95W]

I’m kinda hopIng that @ChatGPT will weigh in on Carson’s speed.

[ChatGPT]

Thank you for providing the link to the research paper. After reviewing the paper, it appears that "Carson speed" refers to the airspeed at which a small aircraft achieves its maximum fuel efficiency.

In the paper, the authors calculate the Carson speed for several different small aircraft using a method called "minimum power speed." This method involves determining the airspeed at which the aircraft experiences the minimum amount of aerodynamic drag, which corresponds to the airspeed at which the aircraft is most fuel-efficient.

To calculate the minimum power speed, the authors used a combination of performance data from the aircraft's flight manual and theoretical calculations based on aerodynamic principles. The authors also assumed that the aircraft was flying at a constant altitude and weight.

Based on the results of their calculations, the authors found that the Carson speed for the small aircraft they studied ranged from 65 to 90 knots, depending on the specific aircraft and operating conditions.

It's worth noting that the Carson speed calculated using the minimum power speed method may not be the same as the optimum cruise speed for a given aircraft, as the optimum cruise speed may take into account other operational considerations such as speed and time to destination. However, the Carson speed can still be a useful metric for comparing the fuel efficiency of different aircraft at a given weight and altitude.

If you are interested in calculating the Carson speed for a specific small aircraft, you may need to consult the aircraft's flight manual or performance handbook to obtain the necessary data on the aircraft's performance characteristics. You may also need to consult with a qualified aviation professional to perform the necessary calculations and ensure that the results are accurate and applicable to your specific operating conditions.

[ChatGPT]

The formula for calculating the minimum power speed, also known as the "L/D max speed," is:

Vmin = √[(2W)/(ρSCLmax)]

where:

Vmin = minimum power speed, in knots W = weight of the aircraft, in pounds ρ = density of air, in slugs/ft³ S = wing area of the aircraft, in square feet CLmax = maximum lift coefficient of the aircraft, which can be obtained from the aircraft's flight manual or performance data L/D max = the maximum lift-to-drag ratio, which can also be obtained from the aircraft's flight manual or performance data.

The minimum power speed is the airspeed at which the aircraft experiences the least amount of drag and therefore requires the least amount of power to maintain level flight. This speed corresponds to the point on the aircraft's power required curve where the power required to maintain level flight is at a minimum.

It's important to note that the minimum power speed formula assumes that the aircraft is in level flight at a constant altitude and weight, and does not take into account other operational considerations such as wind speed or direction, or the effects of turbulence or other weather phenomena. Therefore, the minimum power speed should be used as a starting point for determining the most fuel-efficient cruise speed, and should be adjusted based on the specific operating conditions and requirements of the flight.

 

 

[ChatGPT]

It is not possible to directly calculate the minimum power speed from the best glide speed listed in the POH (Pilot's Operating Handbook). The best glide speed is the airspeed at which an aircraft will achieve its maximum glide distance for a given altitude and weight, and is typically determined by the aircraft manufacturer through flight testing.

However, it is possible to use the best glide speed as a starting point for estimating the minimum power speed, since both speeds depend on the aircraft's aerodynamic characteristics. In general, the minimum power speed will be slightly higher than the best glide speed, since the minimum power speed represents the airspeed at which the aircraft experiences the least amount of drag and requires the least amount of power to maintain level flight.

To estimate the minimum power speed from the best glide speed, you can use a rule of thumb that suggests multiplying the best glide speed by a factor of 1.3 to 1.4. This will give you an approximate range for the minimum power speed, which you can then refine using performance data and other calculations from the POH or other sources.

However, it's important to note that this method is only an estimate, and may not be accurate for all aircraft types or operating conditions. For more accurate results, it is recommended to consult the aircraft's flight manual or performance handbook and use the appropriate formulas and performance charts to calculate the minimum power speed.

The rule of thumb of multiplying the best glide speed by a factor of 1.3 to 1.4 to estimate the minimum power speed is based on empirical observations and generalizations of the aerodynamic characteristics of light aircraft.

The best glide speed is the speed at which the aircraft will achieve its maximum glide distance for a given altitude and weight. This occurs when the aircraft is flying at the speed that maximizes the lift-to-drag ratio, which is also known as the L/D max speed. The L/D max speed is typically slightly lower than the minimum power speed, since the minimum power speed is the speed at which the aircraft will experience the least amount of drag and require the least amount of power to maintain level flight.

The rule of thumb of multiplying the best glide speed by a factor of 1.3 to 1.4 assumes that the aircraft's L/D max speed is approximately 30% to 40% higher than the best glide speed. This generalization is based on the observation that the L/D max speed tends to be slightly higher than the best glide speed for many light aircraft types.

However, it's important to note that the actual relationship between best glide speed and minimum power speed can vary widely depending on the specific aircraft type and operating conditions. Therefore, the rule of thumb should be used as a starting point for estimating the minimum power speed, and should be refined using more accurate methods and performance data from the aircraft's flight manual or performance handbook.

 

 

 

 

[ArtVandelay]

It is not possible to directly calculate the minimum power speed from the best glide speed listed in the POH (Pilot's Operating Handbook). The best glide speed is the airspeed at which an aircraft will achieve its maximum glide distance for a given altitude and weight, and is typically determined by the aircraft manufacturer through flight testing.

However, it is possible to use the best glide speed as a starting point for estimating the minimum power speed, since both speeds depend on the aircraft's aerodynamic characteristics. In general, the minimum power speed will be slightly higher than the best glide speed, since the minimum power speed represents the airspeed at which the aircraft experiences the least amount of drag and requires the least amount of power to maintain level flight.

To estimate the minimum power speed from the best glide speed, you can use a rule of thumb that suggests multiplying the best glide speed by a factor of 1.3 to 1.4. This will give you an approximate range for the minimum power speed, which you can then refine using performance data and other calculations from the POH or other sources.

However, it's important to note that this method is only an estimate, and may not be accurate for all aircraft types or operating conditions. For more accurate results, it is recommended to consult the aircraft's flight manual or performance handbook and use the appropriate formulas and performance charts to calculate the minimum power speed.

The rule of thumb of multiplying the best glide speed by a factor of 1.3 to 1.4 to estimate the minimum power speed is based on empirical observations and generalizations of the aerodynamic characteristics of light aircraft.

The best glide speed is the speed at which the aircraft will achieve its maximum glide distance for a given altitude and weight. This occurs when the aircraft is flying at the speed that maximizes the lift-to-drag ratio, which is also known as the L/D max speed. The L/D max speed is typically slightly lower than the minimum power speed, since the minimum power speed is the speed at which the aircraft will experience the least amount of drag and require the least amount of power to maintain level flight.

The rule of thumb of multiplying the best glide speed by a factor of 1.3 to 1.4 assumes that the aircraft's L/D max speed is approximately 30% to 40% higher than the best glide speed. This generalization is based on the observation that the L/D max speed tends to be slightly higher than the best glide speed for many light aircraft types.

However, it's important to note that the actual relationship between best glide speed and minimum power speed can vary widely depending on the specific aircraft type and operating conditions. Therefore, the rule of thumb should be used as a starting point for estimating the minimum power speed, and should be refined using more accurate methods and performance data from the aircraft's flight manual or performance handbook.

 

 

   

Hey AI chatbot, you’re being repetitive, referring to 1.3-1.4 glide speed 3 times.
I recommend passing your responses through a “editor” function to condense your comments.

[Pinecone]

I think a lot of the issues is that we talk in airspeed instead of AOA.   There is one AOA that results in best glide.  And one that gives you max endurance (minimum fuel flow) and another for max range (miles per gallon).  In jets with AOA gauges, those are marked and you pitch to the appropriate one.

[A64Pilot]

On 5/3/2023 at 2:53 AM, carusoam said:

Where is our Carson Speed Guru?  We sorta have one…  he wrote a master’s thesis on the topic.

let’s invite @testwest to the conversation…

Carson’s speed is the speed you use when ATC sends you in a direction you don’t want to go…

This can happen when flying IFR… and they can’t work you into the system…. They give you a heading 180° away from where you want to go…

No need to fly Mooney speeds to go the wrong direction… 

There is one Mooniac that flew across the country on one tank of gas… efficiency was everything for that trip.

@201er has done some pretty long flights into sparsely populated areas… where fuel economy can become important…

Best regards,

-a-

Actually not, the airspeed you go to when time wasting is the goal, like holding for instance, isn’t Carson’s Speed, it’s max endurance speed which isn’t really even close to Carson’s speed.

While I cannot follow Cobra Drivers math, Carson’s speed can’t be actually defined, because it’s someone’s opinion of an airspeed at which going faster wastes fuel and going slower while conserving fuel wastes time. It can’t be defined or calculated because time is worth different amounts to different people.

The only logical way I could see to define what’s time is “worth” would be to calculate operating costs per hour including all costs not just fuel, but I’ve not seen that done, only then could you argue how much money you saved by flying less hours, even though more fuel was burned, and how much to operate an aircraft will change for each model, so even within the M20 fleet each model would have a “cheapest” speed to fly

An example is let’s say taking engine and prop TBO in account with other items that last x number of hours like vacuum pumps and alternators etc you came up with $50 an hour, on a trip if you fly faster and burned $30 more in fuel, but cut one hour off your flight time going faster you saved $20.

These numbers are made up, but I’d bet money Airlines etc have done that math, or I’d be surprised if they haven’t.

If you go out and graph fuel burn vs speed you will get a graph that’s U shaped, It’s sometimes referred to as bucket shaped, with the two bottom parts of the bucket as “bucket airspeeds” with best glide being the very bottom of the bucket in between the bucket airspeeds.

 

‘So pick any airspeed you want in the bucket, probably those who seek efficiency will pick the forward portion of the bucket, but of course even the “bucket” isn’t well defined as it’s a pretty gentle curve.

[jetdriven]

The thing about aerodynamically clean airplanes is the bucket is not equally shaped at all, it rises in a nonlinear fashion on the low side, and it rises very slow for a good while, and then increases in a nonlinear fashion at a quite high airspeed. I think what that means is Carson speed assumes, a normal drag profile where as the Mooney is cleaner and there's not much penalty for going faster, and usually there's not a whole lotta penalty for going at full throttle and 2500 RPM. Now yes you can slow it down to 55% power and stretch the range by about 15%, but the 40 or $50 an hour it cost the tach hour meter to turn over, is wash with the fuel savings, or even a loss.  65% seems like the cheapest trip cost. 

[A64Pilot]

It’s not difficult to go out and graph your own results, decide for yourself.

My advice is to do it all in one flight to reduce variables and and one altitude and direction. Takes maybe 10 min per test point if you really want to do it right, so less than an hour most likely.

I’d suggest just LOP for all test points, and you guys with AP’s have an advantage. Graph it in 1 gl increments, and at your normal cruise RPM’s as the discussion isn’t as I understand it unusual MP / RPM points, but one that you use because it’s a smooth setting and one your comfortable at.

Carson’s speed for my J down low gives right at 20 NMPG at I think it was 21 squared and LOP at 118 kts indicated at my normal cruise 2,000 or so and 6 GPH

135 kts can be had for 8 GPH and roughly 17 NMPG at 23 squared, no logic in squaring, just she is smooth at 2300 and 2100.

135 is a comfortable airspeed for me and I can keep the cyl temps in the middle of the green, 118 kts and she wallows, control response is slow and it’s difficult to keep the cyl head temp in the green.

So I fly when going on short trips at 8 GPH and 135 Kias or so, and when I travel 2500 WOT and higher altitude usually above 7500 depending on winds.

Those are of course my numbers, yours may differ which is I think the point, what’s a good comfortable efficient cruise for one may not be for another, to some 135 kts would drive them nuts, just too slow.