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Cold weather climb performance: fact or fiction?
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 |
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.. :p 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... |
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 |
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.
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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 |
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.
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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 |
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. :ok: |
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 |
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. :ok: |
excess thrust the same, so rate 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. |
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 |
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. |
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. |
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? |
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. :ok: |
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. |
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. |
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 |
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. |
The only set of charts to which I have regular access are those in the CAP 698 which is published by the CAA for use in JAR ATPL exams. These are reputedly based on a version of the 737, but I know not which.
The engines used in these charts are flat rated up to ISA +15 degrees C. The climb performance charts show a steady decline in climb performance at any given altitude up to the flat rating temperature limit. This is followed by an abrupt increase in performance degradation at higher temperatures. The overall implication of this being that flat rating reduces the detrimental effects of increasing temperatures, but does not entirely eliminate these effects. If we ignore flat rating to simplify the arguments we will see that increasing temperature has two effects. These are a decrease in power available and an increase in power required. The overall result of increasing ambient temperature is therefore a reduction in excess power and hence a reduction in best possible ROC. The principal cause of the reduction in power availabe is the reduction in thrust. In a non-flat rated engine the thrust reduction is caused by a reduction in mass flow due to reduced air density. In a flat rated engine it is caused by the reduced acceleration of the air, which is in turn caused by the increased TAS to CAS ratio. The principal cause of the increase in power required is the increase in TAS at any given CAS. Power required is equal to drag x TAS. If we assume that drag at any given CAS remains constant, then the power required is proportional to any temperature-induced change in TAS. The drag equation includes TAS squared, so multiplying drag by TAS to get power required, gives something that is proportional to TAS cubed. So any increase in TAS at any given CAS will cause an even bigger increase in power required. To visualise the effects of temperature we need to sketch power required and power available curves. Power required looks like a drag curve which has been rotated in an anti-clockwise direction..A bit like a NIKE tick. For a jet aircraft if we simplify the situation by assuming that thrust is constant at all values of TAS, the power available is a straight line starting at the origin (0,0) and moving up towards the top right hand corner of the chart. At low altitude these two lines will cross at two points. At these crossing points the power available is equal to the power required. At all higher and lower speeds the power available is less than the power required. So these two points are the minimum and maximum speeds for which sufficient power is available. At all speeds between the two crossing points the power available is greater than the power required. This excess power can be used to provide a rate of climb. The excess power and hence ROC are proportional to the vertical distance between the two power curves. ROC will be greatest at the speed at which the vertical distance between the two lines is greatest. If we draw a tangent from the origin to touch the under surface of the power available curve we can use this to predict the effects of changes in altitude or temperature. All subsequent power available curves are similar to the first and all curves touch the same tangent. Increasing altitude or increasing temperature cause the power required curve to slide up the tangent towards the right hand end of the chart. The power available curve always starts at the origin because at this point it is equal to thrust multiplied by zero TAS. Its angle is dependent upon altitude and temperature. Increasing altitude and increasing temperarture both cause this curve to rotate clockwise about the origin, thereby reducing power available at any given TAS. The overall effect of these changes is that increasing altitude or increasing temperature will increase power required, reduce power available and reduce ROC. The use of flat rated engines reduces the rate of reduction in power available but has no effect on the rate of increase in the power required. |
Turbofan/Turbojet thrust increases with reduced Compressor inlet temperature, as more work can be done with greater heat input into the compressed airflow. the limiting factor of course being Tmax experienced by the turbine blades (Turbine inlet Temp), which is set by the material they are made of. More thrust=Greater climb performance.
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Thankyou Dorset , excellent post.
Not sure about the climb gradient questions hawk, surely the figures for distance to top of climb represent the gradient? :ok: |
One point I don't follow Keith:
The drag equation includes TAS squared, so multiplying drag by TAS to get power required, gives something that is proportional to TAS cubed. So any increase in TAS at any given CAS will cause an even bigger increase in power required. |
Hawk,
"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? " No, I do not have a V final segment climb gradient chart. All I can tell you from personal experience of around 20,000 hours of operating a variety of jet aircraft with RR, GE and P&W engines, mostly in the tropics, is that climb performance deteriorates with a rise in temperature. |
Wow, Keith, quite the post. You took a tremendous amount of time to write that, an amount of time that will only be surpassed by the number of times I re-read it. I appreciate your efforts.
What still bothers me is that I can make an argument, based on THRUST, and not power, that is still academically unclear to me. Consider thrust changes with tas and temp as being small enough to not be a factor, perhaps as with early non bypass jet engines on a cool day. Regardless of temperature, climbing at V min drag gives a constant amount of excess thrust. This constant amount of excess thrust gives a constant climb angle. This constant climb angle gives a higher rate of climb on cool days than very cold days. I’m still assuming this ACADEMIC argument is 100% logical I’m also assuming that it is not what happens in the REAL world for ONE simple reason. As you pointed out, attaining constant thrust with changes in tas and temperature do not happen. I'm also assuming that if engine manufacturers came up with engine controls that could maintain a constant thrust throughout some defined envelope, that my argument of higher rate on a warmer day, at V min drag would be correct thanks Edited for formatting only |
Even if the excess thrust relationship is unchanged AND the climb rate is unchanged**, the a/c will be at a faster TAS as temp. rises. Faster TAS vs same RoC = shallower angle.
**Of course the RoC will be reduced, making the gradient worse, but for the sake of argument... Hawk, I get the impression you're trying to use a Thrust &/or Power &/or Drag graph for a particular circumstance (WAT) and possibly with unsuitable axis (IAS/CAS?) then applying it in slightly different conditions eg different TAS? Just a thought... |
Even if the excess thrust relationship is unchanged AND the climb rate is unchanged**, the a/c will be at a faster TAS as temp. rises. Faster TAS vs same RoC = shallower angle. |
Tinstaffl, I didn’t say the climb rate is unchanged. In my scenario, which is academic, the excess thrust is unchanged, which implies the climb gradient is unchanged, which implies the ROC is increased for a temp increase. And actually, I wasn’t using any graph, just a 3 step hypothesis that I thought is clear to follow, but difficult to explain. See my previous post.
Oh, I see bookworm posted a reply so yours also. Here's the 3 steps again 1. Regardless of temperature, climbing at V min drag gives a constant amount of excess thrust. 2. This constant amount of excess thrust gives a constant climb angle. 3. This constant climb angle gives a higher rate of climb on cool days than very cold days. Caveat: dealing with a case of near CONSTANT thrust output from the engine, eg non bypass jets. (See Keith's earlier posts about why this is not entirely possible).I use "cool" and "very cold" to avoid the flat rated questions. Bookworm, your question about Keith's post was "Surely the drag depends on the dynamic pressure and therefore the CAS squared?" Not sure what you mean. I get dynamic pressure is .5 * V ^ 2 * p and therefor to tas squared. Drag = thrust required, and P = T x V, so Power is proportional to tas cubed. this help? |
Hawk,
I think that the fault in your argument lies in the fact that the thrust does not remain unchanged as you climb. Thrust is proportional to mass airflow multiplied by the acceleration the engine gives to that air. The acceleration is equal to exhaust velocity minus TAS. As we climb the air density and hence mass airflow at any given engine RPM reduce, causing thrust to reduce. In addition to this, the increasing TAS to CAS ratio causes the acceleration we give the air to reduce. This again reduces thrust. So even if we keep the same CAS and hence the same drag, excess thrust and climb gradient will decrease. This process continues until we hit the absolute ceiling at which maximum thrust equals drag, and excess thrust and best climb gradient are zero. We can visualise this effect by drawing a drag and thrust available curve on a single chart. The drag curve will be the typical bucket shape. If we simplify the situation by assuming constant thrust at all airspeeds, thrust will be represented by a horizontal straight line. (In reality it would be a bucket a bit like the drag curve, but much shallower). At low altitude the thrust line will be some distance above the bottom of the drag curve and will cross it at two points. These are the minimum and maximum speeds for which sufficient thrust is available. Excess thrust is the vertical distance between the two lines and this will be greatest at Vmd. Excess thrust is proportional to best climb gradient so this will occur at Vmd. If we have marked our speed range in CAS we will find that the drag curve does not change with changing altitude. But as explained above, the thrust available will decrease as altitude increases. This can be represented by repeatedly drawing further thrust lines, each lower than its predecessor. When the thrust line just touches the bottom of the drag curve we are at our absolute ceiling. It is tempting to think that we can treat excess power and excess thrust as if they were unrelated. This is not the case. As we climb, the power required increases and the power available decreases. This causes excess power and best ROC to fall to zero at the absolute ceiling. So at the absolute ceiling we have no excess thrust, no excess power, and the best climb gradient and best ROC are zero. Worse than this, there is only one speed at which we have enough thrust and power to fly. For a jet this is speed Vmd. If we repeat the process described above, but this time with power available and power required, we can see how excess power and ROC change. As altitude increases the power required curve keeps being repeated ever higher. At the same time the power available line rotates clockwise about the origin, becoming shallower with each increase in altitude. When the power available line just touches the power required curve we are at the absolute ceiling. We have just enough power to fly straight and level at a single airspeed. If we superimpose the power and drag curves on the same chart we will see that the single speed at which we have enough thrust to fly is also the single speed at which we have enough power. For a jet this speed is Vmd. At this altitude it should really be called Vonly, but for some strange reason it is not. Bookworm, Regarding your comment "Surely the drag depends on the dynamic pressure and therefore the CAS squared?" We need to be a bit careful here. If we change the CAS at any given altitude and temperature it is true that drag is (in part at least) proportional to CAS (or more correctly EAS) squared. But it is more complicated than that, because total drag is made up of induced drag and profile drag. Induced is proportrional to one over EAS squared and profile is proportional to EAS squared. Worse still the coefficient of induced is proportional to one over the fourth power of EAS and the coefficient of profile is more or less constant at most angles of attack. The overall relationship is therefore a bit complicated. But the situation we were considering above was one of increasing temperature. In this case if we keep the altitude constant, we see TAS increases while CAS remains constant. Looking at the drag equation Drag = Cd 1/2 Rho V squared S, the 1/2RhoVsquared is the dynamic pressure and the V squared is TAS squared. The ASI captures dynamic pressure and gives us a CAS indication proportional to it. So if we fly at constant CAS we are flying at constant dynamic pressure. But if temperature increases, the reducing air density Rho must be matched by a corresponding increase in TAS squared, in order to keep the dynamic pressure and CAS constant. This is the cause of the increasing ratio of TAS to CAS as temperature increases. So as temperature increases at any given CAS, the drag stays constant but the TAS increases. Power required is equal to Drag times TAS. As temperature increases at any given CAS, the drag remains constant but is multpilied by an increased TAS. Because TAS appears as TAS squared in the drag, when this is multiplied by TAS to give power required we get something that is proportional to TAS cubed. The same thing happens as altitude increases. |
Keith, reference your quote "I think that the fault in your argument lies in the fact
that the thrust does not remain unchanged as you climb" I’m talking instantaneous climb gradient, instantaneous climb rate. I know that normally thrust decreases as you climb. I’m not trying to suggest this scenario can occur at any other speed other than at, or very close to V md. And certainly, I understand best ROC is at max excess power etc. My scenario has been at ONE altitude, say 1000 ft msl., and only at V md. And, most importantly, with CONSTANT THRUST AS TAS CHANGES WITH TEMPERATURE. I’m still don’t see why my argument isn’t sound. IE 1. Regardless of temperature, climbing at V min drag gives a constant amount of excess thrust. 2. This constant amount of excess thrust gives a constant climb angle. 3. This constant climb angle gives a higher rate of climb on cool days than very cold days What I SUSPECT is the problem, is that the caveat that I’ve put in, that thrust be considered constant with a change in temperature (note, I’m not also adding altitude, since I’m looking at instantaneous gradient/rate) IS TOO FAR OFF from the real world, even in pure jets, to have the effect I’m expecting on gradient, and ROC. |
You are correct that if thrust is constant, and TAS increases through temperature then angle remains constant, and rate increases.
If you were talking rocket engined aircraft this would be usual. To the gas turbine engine a rise in temperature causes a rise in power required to produce the same thrust; T=mv, but kinetic energy is 1/2mv2. A drop in air density with temperature increase, requires an increase in V to maintain thrust. But that is squared into power required, whilst the drop in mass is halved. Then the TAS is increasing so the prop/fan/jet speed must again be increased, again requiring more power yet. An increase in temperature causes an increase in power required, a reduction in power available, requires higher compressor speeds, brings you closer to your EGT limits. So as far as a gas turbine goes you are comparing a reduced power climb on a cool day to a max power climb on a warm day. :ok: |
Keith
I think this TAS cubed thing is just a lack of clarity about what we're holding constant and what we're considering as a variable. We're probably saying the same thing in different ways. Neglecting compressibility, and using a slight variant on your terminology: dynamic pressure = 1/2Rho(TAS)squared = 1/2Rho_standard(CAS)squared (where Rho_standard is a reference constant, density at ISA SL) or TAS = d * CAS where d is the square root of the density ratio. So Drag = Cd * dynamic pressure * area and Power required = Drag * TAS So you can write that as: Cd * 1/2Rho_standard(CAS)squared * TAS * area in other words proportional to (retaining density as a variable) CAS squared * TAS You can, if you want, write this as Power required is proportional to CAS cubed * d or you can write it as Power required is proportional to TAS cubed / d squared But for a constant CAS climb, the key is that the d comes in once not three times. I think the complex shape of the drag curve is a bit of red herring, isn't it? Since lift depends on speed through the dynamic pressure too, the a point at constant CAS on the curves represents a particular drag-to-lift ratio, and therefore, for an aircraft of a particular weight a particular drag-to-weight ratio, regardless of density ratio. Turning that into a power required involves multiplying by the TAS or d only once. hawk I think Keith answered this the first time round, but let me share my understanding of his explanation by putting it another way. The thrust available depends explicitly on both temperature and TAS. Since TAS also depends on temperature for a constant CAS, there is also an indirect dependence on temperature. If thrust is flat-rated, it means that the explicit dependence on temperature is removed. The static thrust (TAS = CAS = 0) will not depend on temperature. But for non-zero CAS, there is still that indirect temperature dependence. Thus the thrust available at climb CAS does vary with temperature even for a flat-rated engine. |
Bookworm,
If we hold pressure altitude and temperature constant then the relationship between CAS and TAS is also constant. Under these circumstances it is true to say that power required is proportional to CAS cubed just as much as it is proportional to TAS cubed. But if we wish to consider real world situations where pressure altitude and temperature change, the ratio of CAS to TAS changes. Under these circumstances it is more useful to say that power required is proportional to TAS cubed. To illustrate this let's use msl and 40000 ft in the ISA. At msl the CAS equals the TAS. At 40000 ft the CAS is about half of the TAS. If we climb from msl to 40000 ft at any given CAS the CAS cubed will be unchanged but the TAS cubed will be 8 times its original value. The power required will in fact only have increased to twice it original value because the density will be about 1/4 of its msl value. Under these circumstances it would be reasonable to say that power required is proportional to Cd x density x TAS cubed. But it would not be at all accurate to say that power required is proportional to Cd x density x CAS cubed. In summary if we keep pressure altitude and temperature constant, then power required is proportional to CAS cubed in exactly the same way that it is proportional to TAS cubed. But if we want to allow for changes in altitude and density we must use TAS cubed. Hawk, I think that I can see what you are saying, but again you are starting with a false assumption. Thrust will not remain constant as temperature increases. It will decrease, causing excess thrust and climb performance to decrease. I suspect that you are using the fact that very high exhaust speeds do not suffer much of an acceleration reduction for each knot of TAS increase. But they still suffer this to some extent. Although we might imagine that the old pure jets would benefit from this effect, they did not do so. This is partly because they did not enjoy the benefits of flat rated engines and partly because increasing temperature reduces thrust in all aircraft propulsion systems (jet or prop). |
The power required will in fact only have increased to twice it original value because the density will be about 1/4 of its msl value. Under these circumstances it would be reasonable to say that power required is proportional to Cd x density x TAS cubed. But it would not be at all accurate to say that power required is proportional to Cd x density x CAS cubed. |
Keith, thanks, and your quote "I think that I can see what you are saying, but again you are
starting with a false assumption. Thrust will not remain constant as temperature increases." I was considering flat rating here. Based on all comments though, I'll assume my scenario would be true if thrust was somehow constant with TAS. But it isn't, and the effect is significant enough that it's effect on my academic scenario is that the reverse is true. I'm done. thanks Bookworm too and all |
Boeing 767 -300 cf6-80
brw 150 tonnes climb to FL 370 ISA +10> clb / 18 minutes over 115 miles ISA +10> clb 2/ (reduced climb) 21 minutes over 132 miles ISA +15 clb / (fulll climb ) 20 minutes over 130 miles ISA +15 clb 2 / 24 minutes over 151 miles ISA +20 clb / 23 minutes over 155 miles ISA +20 clb 2 / 27 minutes over 179 miles clb2 represents a 20% thrust deduction to 10,000 feet decreasing linearly to Max climb thrust at FL 300 I think it is then fair to say that a 5'C rise in temperaure equals a 20% or greater loss of thrust available, and visa versa. :ok: |
Baron, I don't think this figures are any where near V min drag. Also, way out of the flat rating
range. And 20% loss in thrust available with a 5 deg C rise sound WAAAAAAY too much. Was that a published number? For Keith, I have found a thrust vs mach graph for the Garret 731 at sea level, 59 deg F. Its a 2.79 bypass fan. The graph has thrust in lbs on the y axis, and mach on the x axis. The curve starts at 3700 lbs at zero mach, and slopes down to the right. Other values are 2800 lbs at mach .3, and 2200 lbs at mach .6. Concerning thrust decrease with tas near V min drag, say mach .3, about 198 ktas, if I draw a tangent, the slope of the line works out to be 3.4 lbs of thrust per knot. So with a 10 ktas increase near V min drag, the decrease in thrust from the engine is 34 lbs. Based on the 2800 lbs it is producing, this is a 1.2 percent decrease in thrust available. Regarding the excess thrust available, this percent would be considerably higher, of course. Now it you had a model to calculate drag, the decrease in excess thrust due to tas increase could give you the decrease in climb gradient. I’ll leave that up to Baron to calculate |
Hawk37 - when Black Baron talks about a 20% reduction in thrust he is correct. What he has done in his "reduced climb" is derated his engines through the FMC. This allows us to lengthen engine life, reduce wear and tear etc etc. I dont have the figures for the 767 but I do for the aircraft I am familar with, 737-400, from doing my ATPL exams.
The 737-400 comes usually with engines that are flat rated at 23,500lbs static thrust. However we can de-rate the engines to 22k or 20k through the N1 page on the FMC. We do this when we can still safely achieve our performance requirements with the use of less thrust, in order to reduce wear and tear on engine, extend engine life and reduce noise. At London Stansted (where I dispatch) over the last few days daytime temp has not got much over 5 deg celcius. So its pretty much ISA - 10 deg which is great for performance (the fog however isnt great for flying!!!). With a long runway and light pax load we dont need 23.5k, so you can de-rate to 22k. If we went for 20k you can see that we have reduced thrust by approx 15%. On a cold day the air is more dense so the engine produces more thrust. The wing produces more lift because the air is more dense, so the climb gradient is higher. The other thing you need to consider is that performance charts for GRADIENT of climb are only really applicable at low altitude when you want to clear an obstacle in the take off flight patch - ie as at London City, all those big buildings nearby. With a jet airliner what you are really interested in is getting to cruise altitude in the shortest TIME as that make the aircraft more economical. Hence you aim to fly a jet at best rate of climb speed for all but the initial part of the climb. Remeber max angle of climb (GRADIENT) - max altitude gain over shortest distance over the ground. (Vx) Max rate of climb - largest altitude gain for shortest TIME in the air (Vy). On the 737 FMC you can select from the climb page max angle or max rate climb. I think the problem, Hawk37 , is that you are trying to make a hypothetical "text book/labatory" situation fit the real world. Interesting discussion though and useful performance refresher as it was some months ago I sat (and passed) the exam. |
The 737-400 comes usually with engines that are flat rated at 23,500lbs static thrust. However we can de-rate the engines to 22k or 20k through the N1 page on the FMC. .... On a cold day the air is more dense so the engine produces more thrust. |
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