Figuring out Carson’s speed.

[Will.iam]

I was reading the October 2022 Mooney flyer article on how to fly the most efficiently and they showed a chart of how they figured out Carson speed. They showed a best range speed of approx 112 and to take 32% of that to get Carson speed of approximately 139. My question is I don’t have in my POH a best range speed but I do have best glide speed and they claimed that that was the same. But my best glide speed fully loaded is 87kts far slower than the 112 they are showing.  What Mooney model is that chart from? A m20v?

my point is 32% of 87 is 115 far slower than 139 so which is correct?

 

 

 

 

[Pinecone]

MPH versus Knots may be part.

87 knots is 100 MPH

 

But best range is not the same as best glide

https://aviation.stackexchange.com/questions/81664/how-can-l-d-max-be-both-best-glide-speed-and-max-range-speed

 

[PT20J]

Maximum range and maximum glide distance both occur at the angle of attack for [C_L/C_D]_max. This angle of attack will occur at an airspeed that varies with weight.

So, at the same weight, maximum glide distance and maximum range occur at the same speed. In either case, you are getting the maximum distance travelled with the energy available. In the case of glide, the energy available is the potential energy of altitude, and in the case of cruise, the energy available is the chemical energy of the fuel on board.

Carson speed is defined as the speed for minimum fuel flow per unit of velocity and mathematically is the speed for [C_L^1/2/C_D]_max. This turns out to be 1.32 best glide speed.

For derivations, see Anderson, John D., Aircraft Performance and Design, Chapter 5.

Skip

[philiplane]

who buys a Mooney to go slow?

[A64Pilot]

Max range and max glide can be significantly different, what can make it different is the different BSFC of the engine at different power outputs. 

Now people will say a helicopter is different, but it’s not, it just happens that I know it’s numbers well.

The AH-64 max range was 132 kts, pretty much wide open. Min rate of descent was 64 kts, max glide was 98 kts.

An AH-64 is of course a turbine and a turbine very much unlike a piston makes power more efficiently at high power, a piston is most efficient at lower RPM, and LOP of course which is at low power.

But there is nothing magic about Carson’s speed, in fact it doesn’t really exist, all it’s saying is that you can go faster than max endurance which is a different number than max range before fuel consumption begins to climb much faster than speed. It’s simply a number someone I guess named Carson picked that to him was a point that he burned less fuel but fast enough that he wasn’t dog slow.

Go out, run an RPM LOP that’s smooth and quiet and using different MP’s write down IAS and fuel flow, if your really anal graph those numbers.

I used to fly 6 to 6.5 GPH either 21 or 22 squared I forget which and get 120 kts, but I had trouble keeping the CHT in the green and the airplane felt sluggish.

So I now fly 23 squared and 8 GPH and that gives me 130 to 135 kts. airplane doesn’t feel like a dog like it does at 120 kts and I can keep cyl head temps in the green easily. It would be more efficient if I slowed the prop to the bottom of the green and increased MP, but it’s not smooth there on my airplane so I don’t. At this point we are really splitting hairs.

I’m lower altitudes doing this just out flying and not in a hurry.

BTW my best glide speed is 90 kts 90 x 1.32 is 118 kts, which is just too slow for me and I suspect for most.

120 kts gave me 18.5 mpg

135 kts gives me 16.9 mpg.

155 kts is about 14.7 mpg

The 155 is at altitude but the others are down low so I don’t think they compare well, I think at altitude the lower A/S will give better milage than down low. They are true not indicated too.

But go out and graph FF over A/S and find something you can live with, but also pay attention to other factors, like for instance at Carson’s speed my CYL head temp is just barely in the green on an average Fl day and not in the green at all on a Fl winter day.

[PT20J]

1 hour ago, philiplane said:

who buys a Mooney to go slow?

Well, Richard Collins used to say that best power was the only appropriate power setting because we buy airplanes to get somewhere quickly. Of course, gas was cheaper then . 

[A64Pilot]

2 hours ago, philiplane said:

who buys a Mooney to go slow?

I don’t necessarily do it to go slow, but to decrease my fuel costs and it’s my belief increase the life of the engine, plus I’m old and Retired, I’m not necessarily in such a hurry now, so it’s not to go slow, it’s to go efficiently, and often in my mission speed isn’t that big a deal. Often anymore I’m just out OFO, mission is to fly until I’m bored, destination is my departure point, or it’s going to eat breakfast with everything from an Enstrom helicopter, Cubs and 172’s /182’s in a flight with an occasional RV, so pick your speed, no matter what your likely faster than many and slower than some.

To put it in perspective the other day a neighbor and I flew to lunch, that day he happened to be in his Legend Cub and cruising I believe at 80 kts with the O-200 burning 6.5 GPH. He runs everything hard it’s just the way he is.

I can fly 50% faster in a four passenger airplane, with the same fuel burn.

Now if we are traveling I often climb up, leave the throttle WOT and cruise at whatever speed I can get as the mission is to be somewhere, so mission dictates, but I don’t travel as much anymore.

 

[AH-1 Cobra Pilot]

3 hours ago, PT20J said:

Carson speed is defined as the speed for minimum fuel flow per unit of velocity and mathematically is the speed for [C_L^1/2/C_D]_max. This turns out to be 1.32 best glide speed.

For derivations, see Anderson, John D., Aircraft Performance and Design, Chapter 5.

I have not read that book of Anderson's, I have only read the paper someone linked to on another thread.  In the paper, Carson puts together a theory in which he has one too many variables for the number of equations, then does some "hand waving" to come up with the 1.32-term.  Can you copy and post the relevant pages?

[jaylw314]

2 hours ago, A64Pilot said:

But there is nothing magic about Carson’s speed, in fact it doesn’t really exist, all it’s saying is that you can go faster than max endurance which is a different number than max range before fuel consumption begins to climb much faster than speed. It’s simply a number someone I guess named Carson picked that to him was a point that he burned less fuel but fast enough that he wasn’t dog slow.

By that argument, there's nothing magic about Vy, it's just the speed which someone who happened to be interested in climbing fast picked

2 hours ago, bluehighwayflyer said:

@PT20J is correct.  Mooneys weren’t particularly fast airplanes until the long bodies were introduced.  Before that they were purchased for their efficiency.  Carson’s speed is all about efficient travel. It is the speed at which the product of ground speed and MPG is the greatest. It is therefore a natural topic of conversation for Mooney pilots. 

I experimented with Carson’s speed for years in my previous M20J.   Even those who want to fly fast can benefit from using Carson’s speed whenever possible as their climb speed.  

For us poor NA types, Carson's speed IS fast if you're up high.  Around 14-15k' MSL it's about as fast as you can go, and only a bit slower than your max groundspeed. 

[A64Pilot]

13 minutes ago, jaylw314 said:

By that argument, there's nothing magic about Vy, it's just the speed which someone who happened to be interested in climbing fast picked

For us poor NA types, Carson's speed IS fast if you're up high.  Around 14-15k' MSL it's about as fast as you can go, and only a bit slower than your max groundspeed. 

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

[A64Pilot]

5 minutes ago, bluehighwayflyer said:

If I remember correctly, Carson’s formula essentially just produces a cruise speed that, perhaps arbitrarily, equally weights the value of speed and economy.  An equal compromise between the two.  That’s all.  He called it the least wasteful way of wasting.  Of course, Carson’s Speed doesn’t even take into consideration combustion or propellor efficiency, or weather conditions on a specific flight.  Those are entirely different rabbit holes we can allow ourselves to go down.  It’s all fun theory, but I’ll never fly close enough to the edge of the envelope for any of this to ever really matter to me. It’s just a thought exercise.   

That’s pretty much my understanding although I freely admit that I can’t do the math that I’m sure is in the paper and haven’t tried.

It’s a close enough approximation, but how do you equally weigh speed vs economy? Most aircraft have engine TBO’s and those factor into aircraft value, so if you slow down 20% then your flying 20% longer to cover the same distance, so if distance covered is the mission, your shortchanging you engine life / value by 20%, maybe going faster, burning more fuel but flying a shorter time could save money? Too many variables.

The converse of that is this search for speed simply means you get to fly less, so if the mission is to just go fly for an hour why not burn 8 gls instead of 12 or so?

So what I’m abdicating is rather than getting wrapped around the axle trying for this exact speed, if your trying to reduce fuel costs, slow down to an airspeed that’s comfortable and allows the engine to loaf at a lower power but high power enough so that everything is in the middle of the green.

Changes in density altitude, gross weight and your tolerance for going slow will make it so that it’s a variable number.

 

 

[jaylw314]

For future reference, Carson's article is here (I'm sure it's been posted before)

https://www.nar-associates.com/technical-flying/efficiency/AIAA_1980_1847_BHCarson.pdf

1 hour ago, 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.

Carson's speed is defined as the minimum of 'airspeed / gph', and it is proportional to max L/D by the lift and drag equations.  It just happens to always be 3 ^ (1/4) or 1.32 x best glide speed.

In that sense it is more 'real' than Vy, which entirely depends on the vagaries of each aircraft, weight and engine.

Granted, I'd agree Vy is probably more 'important' than Carson's speed, but neither are arbitrary.  Both are specifically defined, even if that doesn't mean you can't choose otherwise.

[PT20J]

The most efficient speed from an absolute point of view would be L/D max. Carson merely noted that this is pretty slow and, although additional speed costs money, we use airplanes to go faster than other modes of transport and time also has value. So, he derived an expression that minimizes the fuel consumed per unit of velocity. That's really all there is to it.

Peter Garrison is better at explaining these things without going through the equations than I am, so I offer his explanation.

The Very Best Speed to Fly.pdf

[PT20J]

2 hours ago, AH-1 Cobra Pilot said:

I have not read that book of Anderson's, I have only read the paper someone linked to on another thread.  In the paper, Carson puts together a theory in which he has one too many variables for the number of equations, then does some "hand waving" to come up with the 1.32-term.  Can you copy and post the relevant pages?

Sure carson_20230416_0001.pdf

[AH-1 Cobra Pilot]

Summary and Conclusions

It is axiomatic that the basis of any physical theory is a set of experimental results. From this it follows that when theory and observation conflict, the theory must be reaxamined. In this paper we have all but abandoned the classical formulation of aircraft cruise performance since, from a practical standpoint, it has little more than academic interest. The optimum fuel efficient airspeed predicted by classical theory is completely at odds with design and operational philosophies. In an attempt to understand why such a disparity exists, it was found that while the definition of the "best" aircraft is arguable, there is, unarguably, a best method of operating a given aircraft which results in a maximum rate of return in airspeed  (hence reduction in flying time) rather than in distance traveled, per unit of fuel consumed.

So, in other words, "I say it should be here!"  Completely arbitrary.

[0TreeLemur]

Carson's speed- or "how to waste fuel optimally".  I did some test flights in my C last year just to explore the concept.  It's just too slow down low.  Who want's to cruise at 16.5" MP (not WOT) and 2350 rpm at 10k?   Yeah, you get over 6:30 endurance and 950 statute mile range, but biological limitations make it infeasible for me at least!

[Austintatious]

On 4/16/2023 at 10:31 AM, PT20J said:

Carson speed is defined as the speed for minimum fuel flow per unit of velocity and mathematically is the speed for [C_L^1/2/C_D]_max. This turns out to be 1.32 best glide speed.

For derivations, see Anderson, John D., Aircraft Performance and Design, Chapter 5.

Skip

I don't know why, but this popped into my head randomly today... I guess it was living rent free.

 

Anyhow, the thought I had is that we dont necessarily care about the minimum fuel flow per unit of velocity... what we should really care about is the minimum DOLLAR flow per unit of velocity.  For this we have to factor gas price AND operating cost per hour.

I may try using chat GPT to create a spreadsheet or formula to calculate this.  This Speed would be different from Carson speed, best economy speed and Min en route speed.  It would in fact be a "best bang for your buck" speed if my reasoning is correct.

 

Edit:  I am having 0 success in getting any sort of actual formula... however on further pondering the matter, I reason that if the fixed operating cost per hour is equal too or  less than the cost of fuel per hour, then Carson speed is still the speed to fly to achieve the least dollars spent per knot of velocity.  If hourly fixed operating cost are greater than fuel per hour cost, then speed would need to increase above Carson speed.   For example, if the fuel cost is 0 and hourly fixed cost are 100 an hour, you would do best to go as fast as possible to achieve the most knots per dollar spent...  Conversely if the Fuel cost anything and hourly fixed cost were 0, then Carson speed would be the most knots per dollar. 

For us Mooniacs,  I believe fuel cost is the bigger cost per hour so if you want to achieve this least dollars per knot  speed, then carson speed it is.

If you fly something which has fixed operating cost in excess of the hourly fuel cost, well, you might be better off flying faster.

Edited April 27, 2023 by Austintatious

[AH-1 Cobra Pilot]

1 hour ago, Austintatious said:

I don't know why, but this popped into my head randomly today... I guess it was living rent free.

 

Anyhow, the thought I had is that we dont necessarily care about the minimum fuel flow per unit of velocity... what we should really care about is the minimum DOLLAR flow per unit of velocity.  For this we have to factor gas price AND operating cost per hour.

I may try using chat GPT to create a spreadsheet or formula to calculate this.  This Speed would be different from Carson speed, best economy speed and Min en route speed.  It would in fact be a "best bang for your buck" speed if my reasoning is correct.

 

Edit:  I am having 0 success in getting any sort of actual formula... however on further pondering the matter, I reason that if the fixed operating cost per hour is equal too or  less than the cost of fuel per hour, then Carson speed is still the speed to fly to achieve the least dollars spent per knot of velocity.  If hourly fixed operating cost are greater than fuel per hour cost, then speed would need to increase above Carson speed.   For example, if the fuel cost is 0 and hourly fixed cost are 100 an hour, you would do best to go as fast as possible to achieve the most knots per dollar spent...  Conversely if the Fuel cost anything and hourly fixed cost were 0, then Carson speed would be the most knots per dollar. 

For us Mooniacs,  I believe fuel cost is the bigger cost per hour so if you want to achieve this least dollars per knot  speed, then carson speed it is.

If you fly something which has fixed operating cost in excess of the hourly fuel cost, well, you might be better off flying faster.

I preceded you by several months in an earlier thread.  For this to be solvable, you still need one more equation, since you input one more variable. 

The bottom line, (as I said earlier), is really, How much will you pay for saved time at the end of your flight?  That will tell you how fast to fly.

[Will.iam]

On 4/16/2023 at 7:15 AM, Pinecone said:

MPH versus Knots may be part.

87 knots is 100 MPH

 

But best range is not the same as best glide

https://aviation.stackexchange.com/questions/81664/how-can-l-d-max-be-both-best-glide-speed-and-max-range-speed

 

The article stated in KIAS not MPH so again where did they come up with 112? Unless the long bodies are that much different than the mid bodies i just don’t see it. Now they did say that was the best range speed again is this shown in the long body poh as mind does not show a best range speed but does show a best glide speed but i get the feeling they are not the same. I wish my poh showed a best range speed as well as the best glide speed. 

[Niko182]

On 4/16/2023 at 10:33 AM, A64Pilot said:

BTW my best glide speed is 90 kts 90 x 1.32 is 118 kts, which is just too slow for me and I suspect for most.

Your best glide speed is 90 KIAS. not KTS. 90 KIAS at 0 ft is 90KTAS. 90KIAS at 18000 is a lot faster than 90KTAS. 118KIAS at 18000ft should land you around 160 KTAS.

[A64Pilot]

On 4/28/2023 at 12:45 AM, Niko182 said:

Your best glide speed is 90 KIAS. not KTS. 90 KIAS at 0 ft is 90KTAS. 90KIAS at 18000 is a lot faster than 90KTAS. 118KIAS at 18000ft should land you around 160 KTAS.

I understand that, however I never fly at FL anything, much less 180.

What happens of course for us N/A guys is that if you climb high enough you end up at Carson’s speed or lower and since your WOT that’s what speed your flying at.

But that’s like arguing that LOP isn’t viable, because in the FL’s your NA airplane can’t make enough power to get there.

Carson’s speed is an arbitrary number, slower and MPG increases, faster and it decreases. Supposedly it’s equally weighted economy and speed, but how do you do that?

It probably wouldn’t be hard to come up with a much higher number than Carson’s speed if in fact TBO of the engine and prop were added to fuel burn.

If you assume 50K for an engine overhaul and 2,000 hr tbo, then that alone is $25 an hour, add in prop and oil changes and someone could likely “prove” it costs less to go faster and burn more GPH because of the lower operating time.

I’m sure the Airlines long ago got this down to a science, but I have no idea what their calculations are, but bet if they could save money by cruising 20 kts slower or faster whether IAS or not they would.

[A64Pilot]

Go out and pick a smooth RPM, then start at some low GPH just LOP let speed stabilize, increase 1 GPH or smaller number if you prefer. At each test point write down GPH and A/S. Then take them and graph them, there won’t be one point that fuel consumption suddenly takes off, it will be a steadily increasing arc that gets steeper as speed increases.

Now if by chance there is one point that shows a definite knee in the curve, then Voila you have found your “best” airspeed, but I suspect you won’t find a definitive knee.

One a similar note, We had a couple of Sportfish over the years and would run out of the Panhandle of Fl to the Middle Grounds, close to the middle of the Gulf, then stay and fish all day Sat and also Sun if we had enough fuel and run all night getting back.

So fuel consumption very much determined fishing time, I had flo scan on both engines and was certain that the point of just breaking onto plane would give me my best MPG, but graphing it showed my gut was wrong. I did it on two different boats, one gas, one Diesel, both were the same, unfortunately there was no sweet spot. So the speed we went out at was determined by how big a hurry we were to get there, faster burned more fuel.

Not saying a boat is an airplane, it’s not, because a boat will float at zero speed, you can’t get behind the power curve on a boat, but can in an airplane, but if you only are interested at above best glide A/S I bet it will be pretty much like the boats were.

If you can handle 118 KIAS then have at it, I can’t just too slow and I can’t keep the engine temps up, and if I abandon LOP to warm up the engine, the. that sort of defeats the purpose doesn’t it?

[Will.iam]

52 minutes ago, A64Pilot said:

Go out and pick a smooth RPM, then start at some low GPH just LOP let speed stabilize, increase 1 GPH or smaller number if you prefer. At each test point write down GPH and A/S. Then take them and graph them, there won’t be one point that fuel consumption suddenly takes off, it will be a steadily increasing arc that gets steeper as speed increases.

Now if by chance there is one point that shows a definite knee in the curve, then Voila you have found your “best” airspeed, but I suspect you won’t find a definitive knee.

One a similar note, We had a couple of Sportfish over the years and would run out of the Panhandle of Fl to the Middle Grounds, close to the middle of the Gulf, then stay and fish all day Sat and also Sun if we had enough fuel and run all night getting back.

So fuel consumption very much determined fishing time, I had flo scan on both engines and was certain that the point of just breaking onto plane would give me my best MPG, but graphing it showed my gut was wrong. I did it on two different boats, one gas, one Diesel, both were the same, unfortunately there was no sweet spot. So the speed we went out at was determined by how big a hurry we were to get there, faster burned more fuel.

Not saying a boat is an airplane, it’s not, because a boat will float at zero speed, you can’t get behind the power curve on a boat, but can in an airplane, but if you only are interested at above best glide A/S I bet it will be pretty much like the boats were.

If you can handle 118 KIAS then have at it, I can’t just too slow and I can’t keep the engine temps up, and if I abandon LOP to warm up the engine, the. that sort of defeats the purpose doesn’t it?

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 

[philiplane]

Carson's speed....meh.

I can buy more gas, but no one can buy more time.

[Fly Boomer]

@philiplane I once read (on MooneySpace I think) "I didn't buy a Mooney to go slow".