Cold weather climb performance: fact or fiction?

[hawk37]

There seems to be the visual perception that for a jet, the colder the temperature, the greater the climb angle and rate after takeoff. Even if one requires the aircraft to be in the same configuration, and thrust (assuming the engines are flat rated throughout the temperature we’re considering), this seems to be the perception. Having pondered this for awhile, I’ve come up with the following, and am asking anyone to help with comments, correct, and generally additional info:

Consider a jet climbing just after take off, clean, at the min drag speed. For noise abatement climbs, I thought this would be close to reality. This calibrated speed should be independent of the OAT.

As for the climb angle, I’m surmising that it must be the same regardless of the temperature. ??

However, on a warmer day, the TAS will be higher, which means the rate of climb is higher on a warm day than a cold day. This seems opposite to the visual illusion.

Any fallacies?

Hawk37

[Runaway Gun]

Freezing Air

Mr Hawk,

Remember the ole formula: Lift=CL 1/2 Rho Vsquared S ??

Well on a colder day, the air is more dense. Therefore the Density part of the formula (Rho) is greater.

Whilst this does achieve more engine thrust, even if this is flat rated, you do get more air flowing over them wings.

Therefore the climb performance does increase markedly, unless the cold weather means that the pilots drank more through the winter to pass away those cold lonely nights, and put on a few extra pounds, which negated all the above..

Hot weather will decrease the climb performance (almost to Nil climb angle) when you are out in the desert on a very hot day.

Strangely enough, the desert heat didn't stop me drinking the nights away either...

[alatriste]

Climbing on a hot day at certain IAS or CAS, associated TAS will be higher and therefore DRAG. If drag is increased, then Power needed will be increase and so, excess of power will be reduced.( even assuming available thrust remain constant cause of flat rated engine operating below reference temperature).
If excess thrust is reduced, then both rate and angle of climb will be reduced when operating on a hot day.
So it is a fact that aeroplanes climb better on cold days.
REGARDS

[Crossunder]

alatriste: drag does not increase that much just because TAS increases (unless you're at high Mno). But, as you say, a higher TAS will require more power, thus decreasing performance on a hot day.

[hawk37]

No fallacy, better climb rate on warm day than cold, at V fs

Further to my original post, an acquaintance has shown me Falcon 50 climb performance that shows at both
V2 and V final segment, the climb gradient DOES NOT vary with temperature, within the flat rating temperatures.
Boeings/airbusses different?
SOOOOO, since V final is practically the calibrated airspeed for minimum drag speed, one can
conclude that the warmer it is, the better the climb rate at that speed. (for flat rated operations).


Runaway
thanks. While I agree with most of your points, I’m not sure they explain the situation I
described, that is an aircraft at min drag speed, within a temperature range that the engines are flat rated.

Reference to your formula, while rho does change with temperature, so does TAS, since the V in your
formula is true airspeed. Warmer day is less rho, but since calibrated airspeed for min drag stays the
same, the tas goes up. This explains why lift then is the same, since we’re talking about same climb angle
and weight.

I’m not sure about "more air flowing over the wings" as you put it. And engine thrust stays the same for
flat rating operation.


alatriste,
However, in this example, the aircraft is climbing at min drag, or put another way at a calibrated airspeed
that allows the most excess thrust. The excess thrust is the same regardless of the temperature, for flat rated operation.
Since the climb gradient is the same, warm or cold, the warmer temperature gives a higher TAS.
Accordingly, the aircraft will climb at a higher rate of climb on a warmer day. Hence the paradox that I think I can explain

Crossunder
Power is not the issue here. We’re talking about the aircraft flying at a speed for maximum excess thrust,
since the aircraft is flying at minimum drag, and hence getting the best GRADIENT.

Drag does not increase if you fly at minimum drag speed, except at high machs.
If excess power was the consideration, then we would be looking speeds for RATE OF CLIMB.

I can only conclude then that jets should climb at a higher rate on a warm
day at V fs, than on a cold day, when flat rated. Further dissentions?

Hawk37

[Runaway Gun]

OK Hawk, you've caught me out. My theory is a little rusty, but my personal experience is that colder days will give better climb performance than hot days. Simple as that.

[hawk37]

Where's Genghis??

Runaway, thats just my point. Sounds "simple as that", yet the math, the performance manuals, the
aerodynamics etc. tell us the gradient is temperature independent, and that the climb rate
will be greater on a warm day. All perception on the other hand, is that climb rate, even angle is
better on a cold day. I alway add the caveat that this is for flat rated thrust, climbing at V
minimum drag, which for most jets is very close to V final segment. No aerodynamicists with some points?
Hawk37

[Black Baron]

The effect of increasing temperature is the same as increasing altitude.

The aircraft will have travelled a lesser distance on a cold day, in the same time span, yet has produced the same thrust, so it must be climbing at a steeper angle.

In the desert jets take forever to groan off the runway and then have very poor climb performance, in Antartica where its well below zero, their CAS is greater than their TAS, so they have excellent climb performance.

[hawk37]

Baron,you say
"The lower the temperature the lower the TAS required for a given CAS, TAS requires thrust. Less thrust required for straight and level means a surplus of thrust."

Not sure what you mean, did you leave a word out?
We're talking minimum drag, so any change in TAS will mean more thrust is required, whether it's an increase or decrease in tas.

There will be no case of "less thrust required", since you already at minimum drag.

I thought my argument was very logical. Is there any sentence you disagree with? Just trying to explain this paradox, that's all. If I'm wrong, belieive me, I'll be the first to agree.

thanks, Hawk37

[Black Baron]

To achieve the same CAS on a hot day as opposed to a cold day, you will have a greater ground speed.
Greater groundspeed equals longer take off run, and a greater distance to achieve the same altitude, which means a reduced angle of climb.
I edited my previous post to remove nonsense which refferred to props and horsepower available. For the same CAS drag must be the same, so thrust required must be the same, excess thrust the same, so rate of climb the same.

[bookworm]

excess thrust the same, so rate of climb the same

Nope, fell at the last unfortunately! Excess thrust at higher speed generates more power, and therefore a higher rate of climb -- just enough, in fact, to compensate for the extra distance travelled and make the gradient of climb the same.

If you take it from the basic equations for equilibrium,

T - D = L*tan(angle_of_climb)

So the angle of climb ends up depending on (T - D)/L

D/L is (near enough) the same at the same CAS, so the angle of climb ends up depending on thrust available.

I know very little about turbine engines, but is the assumption that the thrust is flat rated throught the temperature ranges considered actually true? For example I've got a chart here for a P&W JT4 which is flat rated to 60 degF, after which thrust falls. Perhaps modern turbofans have a wider range.

[hawk37]

Baron, thanks for the reply
ref your quote
"Greater groundspeed equals longer take off run, and a greater distance to
achieve the same altitude, which means a reduced angle of climb "

I’ve meant climb only, no wind, at V min drag, so I’ve not included take off, or ground. Seems we
disagree on the climb angle. My understanding was that it is independent of temperature, for
constant thrust ie flat rated engine. Does anyone have a Boeing or Airbus Final segment chart
to verify this. As I said previously, the Dassault Falcon 50 chart shows this, but it could be wrong.

Your quote
"For the same CAS drag must be the same, so thrust required must be the same, excess thrust the same, so rate of climb the same

I agree with you first two phrases, the third should mean climb gradient the same, no? After
all, it’s excess horsepower that determines climb rate, and excess thrust that determines the climb
gradient. And bookworm seems to agree climb gradient is the same

I still keep getting that the aircraft climbs at a better rate, at min drag with flat rated engines
??

Bookworm, good to hear from you. You must be referrring to barons quote above
My understanding is that flat rated means just that. As temperature would rise, the engine will
speed up in order to maintain the thrust. Until the predetermined temperature, usually ISA plus
something, say isa plus 15, equals 30 deg C. This is at sea level, adjusts for Pressure altitude. I
believe most modern turbofans are somewhat flat rated to isa + 15 deg or more.

I’ve been attempting to show that a flat rated aircraft at min drag speed will climb at a better
rate when the temperature is warm, versus cold. If you say the gradient is the same, which I
thought, then it seems the next logical step is that the rate of climb is higher when warm.

And so, it is just an illusion that the colder it is, the better the rate and gradient. Paradox solved

[Keith.Williams.]

The fact that flat rating gives constant STATIC thrust over a range of ambient temperatures, does not mean that it gives the same thrust at each possible value of CAS. This is because the thrust is related to TAS, which at any given CAS varies with ambient temperature.

For the purposes of POF we often make the simplifying assumption that jet thrust is constant with changing TAS. This is not actually true but for most purposes is "close enough for government work".

Thrust is proportional to the mass flow of air passing through the engines multiplied by the acceleratrion that this air is given by the engines. This acceleration is equal to the exhaust speed minus the TAS of the aircraft. As an aircraft accelerates down the runway the difference between exhaust speed and TAS decreases, causing thrust to decrease. The magnitude of this decrease depends upon the ratio of exhaust speed to TAS. So if we assume that exhaust speed is constant at all ambient temperatures, then anything which increases the TAS at any point in our take-off will reduce the thrust.

As stated previously the sine of the climb angle is equal to (thrust minus drag) divided by aircraft weight. The drag at Vmd is not affected by ambient temperature, but the TAS and hence thrust are affected. As ambient temperature increases, the increasing TAS at Vmd causes thrust to decrease. This decreases the maximum climb angle that can be achieved.

ROC is equal to excess power divided by weight, where power available is thrust x TAS and power required is Drag x TAS. As ambient temperature increases, the increased TAS and reduced thrust at Vmd cause power available to decrease while power required increases. The overall effect is that ROC also decreases as ambient temperature increases.

To understand why some aircraft are affected less than others we need to consider the type of engine used. The degree to which thrust decreases with increasing TAS depends upon the ratio of the exhaust speed to the TAS. In high by-pass engines with their low average exhaust speed each knot of TAS causes a significant drop in thrust. But in a low by-pass or no by-pass engine the higher average exhast gas speed reduces the effect of each knot of airspeed.



Edited by Keith Williams to correct a number of tooping erriots.

[bookworm]

Nice explanation Keith, thank you.

To understand why some aircraft are affected less than others we need to consider the type of engine used. The degree to which thrust decreases with increasing TAS depends upon the ratio of the exhaust speed to the TAS. In high by-pass engines with their low average exhaust speed each knot of TAS causes a significant drop in thrust. But in a low by-pass or no by-pass engine the higher average exhast gas speed reduces the effect of each knot of airspeed.

I guess there's a continuum from almost-constant-thrust turbojet through low-bypass turbofans, high-bypass turbofans to almost-constant-power turboprops.

[hawk37]

So, Keith, if I follow, can you confirm then that you saying that climb GRADIENT at min drag, flat rated, will decrease (slightly) as temp increases
And if so, then can you make a determination on the climb RATE as temp increases, same conditions?

Do the perfomance charts show this climb gradient decrease as temp increases? Boeing/airbus, or both?

Do typical hi bypass engines have enough of a thrust decrease to show this decrease in climb gradient?

many thanks for your time. Your last post must have taken a considerable amount of time. Well done?

[Black Baron]

From the tables for a Boeing 767-300 with GE CF-80 turbofans
CLB 2 (reduced thrust climb power)
weight 160 tonnes
climbing for Fl 370
ISA +10 and cooler 24 mins, 151 nm
ISA + 15 27 mins, 177 nm
ISA + 20 32 mins, 218 nm
at ISA +10 and cooler, it can make FL 390, at ISA +15 it can only make FL 370.
As previously stated, temperature reduces climb performance.

[HotDog]

Figures for 747-200 RB524-D4 engines, brake rel wt 380 tonnes, climb to FL 300
ISA +10 & below - 28mins
ISA + 15 - 34mins
ISA + 20 - 44mins

During climb out of Dubai or Abu Dhabi in the summer, it is not uncommon to hit a temperature inversion at around 1500ft where the ROC drops to zero.

[Tinstaafl]

Even if the engines are flat rated and produce exactly the same thrust at the different temperatures the a/c WILL have a faster TAS for a given IAS as the temperature rises.

A faster TAS requires more power ie more of the engine(s) output is being used ergo less is available to provide climb rate. The lower RoC & the faster TAS results in a reduced AoC.

[hawk37]

Baron, we’ve been referring to climb at V minimum drag, approximately final segment climb speed,
and with flat rated engines. That’s why I had put the phrase "same conditions". Certainly a typical
climb to FL 370 is temperature dependent.
Keiths post seems to nail it pretty well. Having read
it a further 7 or 8 times, it now makes even more sense.
The assumption that thrust is "flat rated" does not apply to changes in TAS. Hence while climbing
at V min drag, which is a calibrated air speed, temperature increase causes a measureable loss in
thrust available, for other than pure jets.
Secondly, if I understand him correctly, there is an increase in Power required (note that Thrust required
will stay the same) due to the increase tas as temperature increases.
Third, and I’m not 100% sure of this, (KEITH can you help here) there is an effect on Power
available, as temperature increases, due to the increase tas. (P=T x V). thrust may slightly
decrease due to tas increase as temp rises, but velocity in the formula also has an INCREASE. I
think Keith is saying that the total effect on Power available though is that it decreases.

I’d say the jury is out. Even at V min drag, expect a decrease in the climb gradient

for BARON and HOTDOG,

Do either of you two have a V final segment climb GRADIENT chart, and are you capable of providing
any figures on how much the gradient changes based on temperature?

For simplicity, it looks like Dassault publishes their’s as a straight line, ie no change in climb
gradient with temp, when considering the flat rated portion of engine operation

Does anyone has a link showing Power available, required, and Thrust available, VS velocity,
for different TEMPERATURES?

Many thanks for your efforts

[bookworm]

The figures Baron and HotDog quote demonstrate that the engine is not capable of supplying that flat-rated thrust (static or otherwise) over the entire temperature and altitude range.

What would be more useful would be figures indicating the climb gradient at sea level over a range of temperatures.