Takeoff distance versus ambient temperature

[jrh]

I've recently run across a performance oddity that nobody has been able to explain. I've spoken to several friends, senior pilots at my company, and even a check airman at a major sim center and nobody has come up with a good explanation. In fact nobody had even noticed this oddity until I asked them about it.

Looking at the takeoff distance charts for one of the planes I fly, one would expect to see takeoff distances increase with ambient air temperature, all other factors remaining equal. This is exactly how it works at higher gross weights. For example, at roughly 16000 lbs, for a given set of conditions, you might see something like this:

-20 degrees = 3000 feet
0 degrees = 4000 feet
20 degrees = 5000 feet
40 degrees = 6000 feet

Obviously these are fictional numbers, but you see the trend...warmer air requires more runway, which is what most pilots expect.

Now, the oddity starts appearing as gross weight decreases. At a "mid" gross weight, say, 13000 lbs, you'll see a small, momentary reversal during a range of temperatures. It looks like this:

5 degrees = 2600 feet
10 degrees = 2800 feet
15 degrees = 2700 feet
20 degrees = 2750 feet
25 degrees = 3000 feet

See how if you were to graph this, it would look like an "S" in the graph?

Continuing to an even lower gross weight, at the very light end of the spectrum, say, 10000 lbs, you see something extremely odd:

-25 degrees = 2200 feet
0 degrees = 2500 feet
20 degrees = 3000 feet
40 degrees = 2600 feet
50 degrees = 2200 feet
54 degrees = 2100 feet

See how a graph would essentially be a "hump" of some kind in the middle of the temperature range? What's even more bizarre, you literally get better takeoff distances at +54 degrees than -25 degrees.

Again, I've made up the numbers in this post, but the trend is what I'm talking about. It occurs regardless of field elevation.

Any idea what causes this? Considering it only happens at lower weights, I suspect it has something to do with the power to weight ratio.

A friend suspected it might have something to do with braking action being relatively constant across the temperature spectrum, yet vast differences in power available, therefore at the cold end of the spectrum the balanced field length is more dependent on the braking ability, whereas on the hot end of the spectrum the distance is more determined by the power available from the engines. I noticed V1 is constant at cooler temps, then begins dropping several knots at the upper end of the temperature spectrum.

Seems odd to say, "It's too cold to takeoff, I hope it warms up a few degrees," but that's exactly what I had to hope for the other day!

 

[Markf64]

It seems to me that if, as you say, everything stays the same except for temperature, that as temperature increases, so will the amount of runway needed...basic physics.

Maybe the manufacturer, who wrote the manual has an explanation. A very interesting question.

 

[mikecweb]

Engine derate/flex?

 

[bimmerphile]

Is this a turboprop or a jet?

 

[jrh]

Is this a turboprop or a jet?

Older Citation.

 

[jrh]

Engine derate/flex?

We don't have flex numbers on this aircraft, and as for derating the engine, I have no idea what the original specs were.

Even supposing it was related to engine limits, could you elaborate on what would cause these trends? Have you ever seen them before?

 

[bimmerphile]

I'm guessing it's Vmcg related to density altitude

 

[Deleted member 27505]

I've recently run across a performance oddity that nobody has been able to explain. I've spoken to several friends, senior pilots at my company, and even a check airman at a major sim center and nobody has come up with a good explanation. In fact nobody had even noticed this oddity until I asked them about it.

Looking at the takeoff distance charts for one of the planes I fly, one would expect to see takeoff distances increase with ambient air temperature, all other factors remaining equal. This is exactly how it works at higher gross weights. For example, at roughly 16000 lbs, for a given set of conditions, you might see something like this:

-20 degrees = 3000 feet
0 degrees = 4000 feet
20 degrees = 5000 feet
40 degrees = 6000 feet

Obviously these are fictional numbers, but you see the trend...warmer air requires more runway, which is what most pilots expect.

Now, the oddity starts appearing as gross weight decreases. At a "mid" gross weight, say, 13000 lbs, you'll see a small, momentary reversal during a range of temperatures. It looks like this:

5 degrees = 2600 feet
10 degrees = 2800 feet
15 degrees = 2700 feet
20 degrees = 2750 feet
25 degrees = 3000 feet

See how if you were to graph this, it would look like an "S" in the graph?

Continuing to an even lower gross weight, at the very light end of the spectrum, say, 10000 lbs, you see something extremely odd:

-25 degrees = 2200 feet
0 degrees = 2500 feet
20 degrees = 3000 feet
40 degrees = 2600 feet
50 degrees = 2200 feet
54 degrees = 2100 feet

See how a graph would essentially be a "hump" of some kind in the middle of the temperature range? What's even more bizarre, you literally get better takeoff distances at +54 degrees than -25 degrees.

Again, I've made up the numbers in this post, but the trend is what I'm talking about. It occurs regardless of field elevation.

Any idea what causes this? Considering it only happens at lower weights, I suspect it has something to do with the power to weight ratio.

A friend suspected it might have something to do with braking action being relatively constant across the temperature spectrum, yet vast differences in power available, therefore at the cold end of the spectrum the balanced field length is more dependent on the braking ability, whereas on the hot end of the spectrum the distance is more determined by the power available from the engines. I noticed V1 is constant at cooler temps, then begins dropping several knots at the upper end of the temperature spectrum.

Seems odd to say, "It's too cold to takeoff, I hope it warms up a few degrees," but that's exactly what I had to hope for the other day!

Can you please post the real numbers you're citing, and the specific type and its year of manufacture? It's rather useless to ponder this in the abstract.

 

[jrh]

I'm guessing it's Vmcg related to density altitude

Interesting idea. I hadn't even considered this.

Since Vmcg must be less than V1, are you implying V1 is possibly set higher under cold conditions, which results in a longer distance required in the event of an abort just prior to V1?

 

[bimmerphile]

Yes. Engine and aerodynamic performance is better at lower density altitudes, but they're probably not limiting at the higher weights initially quoted. That might be accelerate stop. The higher temp and lower weight is most likely vmc, as performance decreases with temperature increase.

Not a cfi, just a guess

 

[jrh]

Can you please post the real numbers you're citing, and the specific type and its year of manufacture? It's rather useless to ponder this in the abstract.

It's a Citation V. I won't be at work again for several days so I don't have the exact numbers readily available. I suspect these trends could probably be seen in other 500-series Citations, but I haven't checked yet.

I don't see how specific numbers will make much of a difference to the discussion though. I could explain the general concept of a balanced field length without specific numbers. That's all I'm looking for here. A general explanation for why a takeoff distance required will not always be intuitive to the conditions.

 

[mikecweb]

We don't have flex numbers on this aircraft, and as for derating the engine, I have no idea what the original specs were.

Even supposing it was related to engine limits, could you elaborate on what would cause these trends? Have you ever seen them before?

If you have a reduced power takeoff at higher temps the reduction would be less. Basically I've seen the temp drop a few degrees run new numbers, now our stop margin is less but our power setting has been reduced as well maybe flaps too.

But that all doesn't apply if you aren't doing reduced power takeoffs. I like the VMCG answer.

 

[Markf64]

If you have a reduced power takeoff at higher temps the reduction would be less. Basically I've seen the temp drop a few degrees run new numbers, now our stop margin is less but our power setting has been reduced as well maybe flaps too.

But that all doesn't apply if you aren't doing reduced power takeoffs. I like the VMCG answer.

I like the VMCG explanation too. It's great to learn something new from time to time here on JC. I am interested to hear the whole story.

 

[Corporate Pilot]

I researched data for our Ultra and I believe at the lower weights it is a combination of VMC and the engines being derated. Vmca is 95K and Vmcg is 91K. From a BCA article on the Ultra "The -5D is the most highly evolved of the -5 series, a 3,350-pound thermodynamic rated turbofan that is flat-rated at 3,045 pounds of thrust for takeoff to 27°C (80°F)." If you look at the 11.5 weights, see attachment, the runway numbers and V speeds start going down after temperate goes above 20C. I am assuming as the temp goes above 27C and the engines produce less power Vmc is going down allowing the use of lower V speeds. I do find it interesting that Vr is below Vmca starting at 13.5.

 

[jrh]

I do find it interesting that Vr is below Vmca starting at 13.5.

Very interesting indeed.

I see the Part 25 certification requirements actually say Vr must be at least 105% of Vmc, meaning the Ultra shouldn't have a VR of less than 100 knots most of the time. Only the Vr numbers all the way up at 16.3 comply with this.

Maybe they got a waiver for this requirement? If so, how and why?

 

[bimmerphile]

I researched data for our Ultra and I believe at the lower weights it is a combination of VMC and the engines being derated. Vmca is 95K and Vmcg is 91K. From a BCA article on the Ultra "The -5D is the most highly evolved of the -5 series, a 3,350-pound thermodynamic rated turbofan that is flat-rated at 3,045 pounds of thrust for takeoff to 27°C (80°F)." If you look at the 11.5 weights, see attachment, the runway numbers and V speeds start going down after temperate goes above 20C. I am assuming as the temp goes above 27C and the engines produce less power Vmc is going down allowing the use of lower V speeds. I do find it interesting that Vr is below Vmca starting at 13.5.

Where are you getting the numbers for vmca and vmcg from? I think vmca is somewhere between v1 and vr, since it's assumed in an engine failure at that weight at v1 that the aircraft will still continue to accelerate on 1 engine. It would be a bit silly to go flying below vmca

 

[Corporate Pilot]

Where are you getting the numbers for vmca and vmcg from? I think vmca is somewhere between v1 and vr, since it's assumed in an engine failure at that weight at v1 that the aircraft will still continue to accelerate on 1 engine. It would be a bit silly to go flying below vmca

CAE and SimCom training manuals I have on my laptop. Takeoff numbers came from CAE checklist.

 

[bimmerphile]

CAE and SimCom training manuals I have on my laptop. Takeoff numbers came from CAE checklist.

Vr isn't permitted to be less than 105% of vmc per the part 25 certification standards, so I'm not quite sure where the figures came from. I don't know if there is such a thing as a waiver for that.
as an aside, whats the deal with the table at the top of the chart you posted about thrust? Is the SE climb thrust lower than takeoff? Idk much about business jets, just curious.

 

[jrh]

as an aside, whats the deal with the table at the top of the chart you posted about thrust? Is the SE climb thrust lower than takeoff? Idk much about business jets, just curious.

In the Ultra, max takeoff power is limited to five minutes of use during normal operations, or ten minutes under emergency conditions I believe. In the event of an engine failure, max continuous power is the number to use on the operative engine for climbout. It's slightly lower, but has no time limit.

 

[CFI A&P]

The Vmcg angle is interesting however, I’d noticed the hypothetical performance numbers are near the range requiring anti-ice for certain conditions. Are there any notes on the charts related to anti-ice or operations at temperatures less than 10c and with visible moisture ?


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