Turboprop vs Jet climb speeds?

[VPI Greenwood]

Can anyone help me with a question of best climb speeds for turboprop aircraft such as the P3?

In a turbojet, I was taught that best angle of climb occurs at Min Drag speed, and the best rate something higher than this, due to increased ram effect in the engines and more lift.

Does this latter point also apply to a turboprop? Anecdotally I have found that a good climb rate can be obtained in the P3 at 250 kts indicated airspeed - in excess of the recommended 220kts.

[Keith.Williams.]

VPI,

The short answer to your question is no, there is of course (inevitably) a rather longer one.

BEST ANGLE OF CLIMB
Excess thrust is thrust minus drag. The maximum attainable angle of climb is proportional to the excess thrust divided by the weight. So maximum angle of climb occurs at the speed at which excess thrust is greatest.

For both jet and prop aircraft the total drag curve is typically a bucket shape with the minimum value at VMD.

Thrust in a propeller aircraft drops off quite quickly due to decreasing propeller efficiency as speed increases. So the greatest excess thrust and hence best angle of climb occurs at quite a low speed. Strictly speaking this is at the lowest safe flying speed but a slightly higher speed is usually recommended.

In a low bypass (or no bypass) jet the thrust stays almost constant as speed increases. This is because increasing thrust due to ram effect compensates for decreasing thrust due to momentum drag. The overall effect is that thrust typically falls off as speed increases, levels off at about 250 Kts then increases at higher speeds. The actual figures obviously vary with engine type. So with almost constant thrust, the greatest excess thrust and hence best angle of climb occurs at the minimum drag speed VMD.

MAXIMUM RATE OF CLIMB
Maximum attainable rate of climb is equal to excess power divided by weight. So maximum rate of climb occurs at the speed at which excess power is greatest.

Excess power is power available minus power required. Power available is thrust multiplied by TAS. Power required is drag multiplied by TAS. For both jets and props the power required is rather like the drag curve, but somewhat steeper at the high speed end.

In propeller aircraft the thrust falls off rapidly with speed as TAS increases. So multiplying the two together gives a curve rising from zero at zero TAS, reaching a maximum at a fairly low TAS, then decreasing at higher speeds. So the best excess thrust and best ROC occurs somewhere close to ( but not actually at) the top of the power available curve.

For a jet the thrust is almost constant, so multiplying this with increasing TAS gives an almost linear increase in power available, as speed increases.

If you examine a typical power available/power required diagram you will see that the best rate of climb speed for a jet is much higher than that for a prop. Ram effect is proportional to the square of the TAS. So although a turbo-prop will benefit from some ram effect, its much lower speed means that this benefit will not be as great as that affecting a jet. With very advanced (high speed) propeller aircraft this gap will of course be narrower.

Such a diagram will also illustrate why your P3 climbs quite well at 30 Kts above the recommended best climb speed. The power available and power required curves are pretty well parallel close to the best climb speed. So you can deviate from it a little bit without losing too much ROC. If you look now at the curves for a jet, the situation is even better. Because the power available curve is almost straight. You can achieve something very close to the best ROC over quite a wide speed range.

(I tried to paste a diagram into this message but it got lost along the way)

[Checkboard]

[quote]Thrust in a propeller aircraft drops off quite quickly due to decreasing propeller efficiency as speed increases. So the greatest excess thrust and hence best angle of climb occurs at quite a low speed. Strictly speaking this is at the lowest safe flying speed but a slightly higher speed is usually recommended.<hr></blockquote>

Hmmm.. depends upon your definition of "lowest safe flying speed" I suppose, but you can fly quite safely near the stall, and have very little excess thrust, and almost no climbing ability.

[donpizmeov]

VPI,
The P3 is a great airplane. In the colder climates (Greenwood!) it has plenty of horsepower, and yes will climb nicely at higher speeds. However warm it up (Butterworth, Malayasia), and reduce the available horsepower and the story does change. Much above 220kts and it would have a hard time climbing when above 10000'. If I remember correctly, the speed had to reduce 2kts per 1000' above 10000'? This was Ok but I use to stop the reduction at 200kt IAS and this seemed to work OK.
To get away from the ground in the quickest time, a climb at normal rated power, clean and 1.52Vs works a charm if light or cold, and V504/V2(slowest safe speed Vs excess thrust) if heavy and hot (the differance being the time to accelerate to the higher speed and retract flaps).
But the more important question about P3 ops, is how to ensure the FLTENG buys the first round of drinks at the end of the flight!
Don

[A and C]

At average weights we found that the Electra would climb well at 250KT up to about FL120 when it hit 500ft/min then i would peg V/S untill the speed came back to 210 KT and at was as high as you would want to go on a short leg , after an hour or so a step climb might be in order ,I am left to speculate that the reason that the older turboprops used about 210 KT was to fit in with the piston engine traffic of the day.

As a comparison the B737-800 econ climb speed is about 300KT.

[JJflyer]

The threeholer. B727-100 with -7´s that is. You´ll get about 1500 to 2000 ft/min wether you climb @ 250 KIAS or 350 KIAS.This works up to the 20´s depending on weight and temperatures.
Once you point your nose to your destination you´ll get there a lot quicker at the higher speed. Overall trip fuel consumption is actually a little lower due to the saved time.

[Keith.Williams.]

Checkboard,

You're absolutely correct. Most texts quote the "lowest safe flying speed above unstick speed".

I'd hate to be responsible for any smoking holes caused by people investigating climb performance at VS.

Thank you for that.

The crux of the original question is that ram effect follows an exponential curve. propeller aircraft don't go fast enough to get very far up the curve, but do suffer from loss of thrust and propulsive power due to decreasing propeller efficiency. The question of what exactly is driving the prop (piston or turbine) doesn't really change this much.

[A and C]

If you use V/S in the climb then you must keep your eye on the ball and know at what speed to call a halt to the practice or as you say a "problem" will result !.

[VPI Greenwood]

Thanks for the interesting points so far...

Is it safe to say that once climbing at Vmd, a reduced climb rate would surely result with a decrease of airspeed and therefore increase in drag? I have observed people climbing on a hot day and continuing to ease the nose up (well below min drag speed)trying to get to height.

The other aspect of climb speeds I'm interested in is simply the idea of gaining more lift at increased speed - lift increasing with the square of the speed and all that.

A and C - I was interested in your line about 'fitting in with the piston aircaft of their day ' - this sounds familiar as one of the senior P3 (Aurora)pilots at Greenwood told me that the reason for the existing climb schedule was to 'maintain an average TAS in the climb' ! This didn't sound particularly scientific to me!

Donpizmeov - I concur about the FE buying the first round! Can you confirm that 1.52Vs equates to Vmd? Do you recall the 190 kts for 3 Eng at all weights? This 190 kts seems bizarre to me as often it puts the pilot well below the 1.52Vs. Again anectdotally (and in the simulator) I have found a better 3 engine climb above the 190kts recommended.

[Stagnation Point]

VPI

YOu don't climb better at higher speeds because you are producing more lift. Go back to your diagram that shows the forces acting on the acft in a climb, or S&L flight. Lift will always = weight and has little to do with the rate of climb at a steady state. You will notice that the faster you fly the lower the attitude will be which means that you have a lower AOA, AOA directly affects Co efficient of lift which if you multply that by your, 1/2 rho V Squared S, part of your lift formula then L = W. Increas V decrease AoA. In a climb the Trust and drag lines are inclined so some thrust will carrying some of the weight of the acft. In other words it doesn't matter how fast you are flying, in a steady state L=W and T=D. In a climb the excess thrust = ROC.

Enjoy your time on teh P3, I only managed a few years on it but thoroughly enjoyed every minute of it. When people go on about real acft they are talking about the P3.

[Tinstaafl]

erm......in a steady state climb L &lt; W, with a component of T making up the deficit.

[Keith.Williams.]

VPI,

Before taking your comments in turn, it might be worthwhile taking a moment to examine what happens in a steady climb.

The most important point to note is that lift is less than weight in a steady climb. This can be illustrated by considering an aircraft with a thrust:weight ratio of considerably more than 1. In level flight the wings carry all of the weight, so wing lift equals weight (if we ignore forces produced by other parts). In a vertical climb (nose pointing straight up) the thrust carries all of the weight. So the wings must produce zero lift. This means that in a steady climb the lift must be equal to the (weight x the cosine of the angle of climb). And the thrust required is equal to the drag plus (weight x (1 - the cosine of the angle of climb)).

Excess thrust is that part of the thrust that is not being used to oppose the drag. So in a steady climb the excess thrust is equal to that part of the weight that is being carried by the engines. The greater the excess thrust, the greater will be the proportion of the weight that can be carried by the engines, and hence the greater the angle of climb. So the best angle of climb is achieved by flying at the speed at which excess thrust is greatest.

To understand why rate of climb is related to excess power we need to remember that power is the rate at which work is done. When an aircraft climbs work is done in two ways; To push it forward against the drag and to increase its altitude. The total work done is equal to the (drag x distance moved through the air) plus the (weight x the increase in altitude). So the rate at which work is done or power is expended, is (drag xTAS) plus (weight x ROC).

The fist part of this (the drag x TAS) is the power required to maintain TAS. The second part (weight x ROC) utilises the remaining (or excess) part of the power available. Excess power is the power available minus the power required to maintain TAS. Only this excess power is available to increase altitude. Now if power expended in increasing altitude is equal to (weight x ROC), then ROC is equal to the excess power divided by the weight. So for any given weight the best ROC is achieved at the speed at which excess power is maximum.

Now taking your comments in turn.

Quote - Is it safe to say that once climbing at Vmd, a reduced climb rate would surely result with a decrease of airspeed and therefore increase in drag…

It depends on the type of aircraft (or rather propulsion system).

TURBOJET AIRCRAFT
For a turbojet with its almost constant thrust, best angle of climb occurs at Vmd. Any increase or decrease in speed will increase drag, reduce excess thrust and reduce angle of climb. This is because (as you imply) if drag increases and thrust is constant then excess thrust and angle of climb will decrease.

But the best rate of climb requires best excess power and this occurs at a higher speed (about 1.32 Vmd). So increasing speed above Vmd initially increases ROC up to its optimum value, then decreases it.

PROP AIRCRAFT
For a prop aircraft thrust decreases rapidly as speed increases. So although Vmd gives the lowest drag it does not give the highest thrust or excess thrust. Best angle of climb occurs at a speed (Vx) slightly lower than the minimum power speed Vmp. When decelerating from Vmd to Vx, thrust increases faster than drag. So angle of climb increases up to its optimum (at Vx) then decreases again. ROC depends upon excess power. Although Vmd gives minimum drag, the minimum power required occurs at the considerably lower speed of Vmp. So when decelerating from Vmd, ROC increases up to its optimum at the best ROC speed (Vy), which is just above Vmp, then decreases again at lower speeds.

So for your P3. whether you are after best angle of climb or best ROC, you should be flying slower than Vmd. Both increasing altitude and increasing ambient temperature increase the power required and decrease the power available. The overall effect is a reduced ROC and a reduced best ROC speed.

Quote - …..gaining more lift at increased speed - lift increases with the square of speed ….
It is true that if you increase speed whilst maintaining a constant angle of attack, lift will increase, causing the aircraft to climb. But this is not going to produce either the best angle of climb nor the best rate of climb. The problem is that at speeds above Vmp, the greater lift comes at the expense of greater power required. At speeds above Vmd the greater lift comes at the expense of higher drag, which means higher thrust required.

TURBOJET AIRCRAFT
For turbojets the thrust is almost constant speed and the power available increases almost linearly with increasing speed. So as speed increases towards Vmd, the reducing drag increases excess thrust and angle of climb. As speed increases above Vx (which is Vmd), the increasing drag reduces both excess thrust and angle of climb. As speed increases up Vy (which is slightly higher than Vmd), rate of climb increases, then decreases at higher speeds.

PROP AIRCRAFT
For propeller aircraft thrust decreases from the moment you let the brakes off and power available increases up to some speed between Vmp and Vmd then decreases at higher speeds. So as speed increases from Vx (just below Vmp) the angle of climb decreases and above Vy (just above Vmp), the rate of climb also decreases.

Quote ….. This (3 engine) 190 Kts seems bizarre…..
I cannot comment on speeds that are specific to the P3 but your query regarding the 3 engine best climb speed appears to illustrate the way asymmetric power alters Vmd, Vmp, Vx and Vy. With one engine out the drag is increased due to the dead prop (even when feathered) and the increased trim drag caused by the need to overcome asymmetric thrust. This increases both drag and power required, but decreases Vmp, Vmd, Vx and Vy. The overall effect is a reduced best angle of climb and ROC and reduced best climb speeds.

The magnitude of these effects depends upon which engine has failed. Assuming each is able to produce the same thrust and power, then the one which causes the greatest asymmetric thrust will cause the greatest reduction in climb performance and the lowest best climb speed. Assuming the P3 has right handed propellers (not counter or contra-rotating), then the left outer will have the biggest effect and the right inner (I think) will have the least effect. The figure of 190 Kts you quote might simply be the average or worst case figure. You could test this in the simulator by noting the ROC when trying different combinations of failed engine and speed. If I am right you will find that climb rate and best climb speed are highest with the right inner dead and lowest with the left outer dead.

[VPI Greenwood]

Thanks again for comrehensive & aerodynamically educational replies - particularly the Keith Williams email graph!

I'm going to repost a couple of person-specific questions....

Donpizmeov - I concur about the FE buying the first round! Can you confirm that P3's 1.52Vs equates to Vmd? Do you recall the P3's 190 kts for 3 Eng at all weights? This 190 kts seems bizarre to me as often it puts the pilot well below the 1.52Vs. Again anectdotally (and in the simulator) I have found a better 3 engine climb above the 190kts recommended.

A and C - I was interested in your line about 'fitting in with the piston aircaft of their day ' - this sounds familiar as one of the senior P3 (Aurora)pilots at Greenwood told me that the reason for the existing climb schedule was to 'maintain an average TAS in the climb' ! This didn't sound particularly scientific to me!
Any thoughts...?

Thanks!

[donpizmeov]

VPI,
V52 is pretty close to Vmd. The actual number would be loiter minus 10 to 15kts. Remember that loiter is faster than Vmd to allow for turns, poor handling, FATIGUE etc. This is why endurance can be increased dramaticly by flying three eng sub loiter (loiter minus 10 to 15 kts depending on weight). In fact the P3 can do better on three engine sub-loiter than on two engines at loiter, and its better for the peace of mind as well!But V52 was on the placard right in front of me so I would use that when the Flteng had not placarded the loiter speed. I have forgetten the formula to work out loiter, but try a few for certain weights and then compare this to the V52 speed.
Re the 190kt three engine climb: I remember reading a Orion digest once that stated that it was wise to climb to altitude at 190kts on three engines as this was nicely within the restart envelope for the T56 engine/prop combination. I always thought this strange as alot of the time a relight was out of the question, and no other speeds were offered. But I guess it is a good comprimise, and having only one speed for all occasions keeps it simple. I will hunt around and see if I still have any of those digests that I stole (errh borrowed), but I think they were all handed away when I departed all things VP for things Boeing.
Another speed I thought handy to remember was that at 200kts double assy the feet could be rested from the rudder pedals as the rudder trim would now hold all the force.
Now where is my VPI mag?
Don

[VPI Greenwood]

Don

Email me your postal address and we'll put you on the list for this year's issue - out about April/May!

Cheers

[donpizmeov]

Thank VPI. I have done just that. Is Harry Vincent still on the CP140?
Don