Temperature anomalies

[ThomseN_inc 1,128]

Hi,

 

I was doing flights from/to Addis Abeba (HAAB) the last days and ran into some (i believe) issue with the outside air temperature. Last flight for example i was taking off with a TAT of 16 degrees at ground level (field elevation is around 7500 feet) and during initial climb the TAT suddenly started rising to around 25 degrees in about 2 minutes. It then startet do decrease again and i reaced 0 degrees at around FL300 which obviously resulted in a pretty bad climb performance (PMDG 738). I know Addis Abeba is hot and high but this seemed a bit off to me.

Has anyone else seen similar things lately?

 

Best regards

[sd_flyer 6,087]

Temperature inversion?

[ThomseN_inc 1,128]

12 minutes ago, sd_flyer said:

Temperature inversion?

But 0 degrees at >FL300? 

[martinboehme 522]

I don't think there's anything wrong here. All of these values look plausible.

It's important in this context that TAT (total air temperature) is not the same as the temperature of the free air outside the aircraft -- that would be SAT (static air temperature). When the aircraft is in flight, TAT is higher than SAT; the difference between the two is called ram rise, and it increases with speed. This Wikipedia article contains more details:

https://en.wikipedia.org/wiki/Total_air_temperature

Here are two rules of thumb for calculating TAT for a given SAT and speed (either in knots or Mach number):

TAT = SAT + (TAS / 87)^2

TAT = SAT * (1 + .2 M^2)

(For the second formula, the temperatures need to be in Kelvin.)

For your first scenario, in the initial climb, let's assume SAT is still the same as it was on the ground, and that you have a speed of 250 knots. This gives us:

TAT = 16 C + (250/87)^2 = 24 C

This is in pretty good agreement with your observation.

For the second scenario, let's work backwards from your observed TAT to work out what the SAT is. A TAT of 0 C is 273 K, and I'll assume that you're cruising at Mach 0.8. We get

SAT = TAT / (1 + .2 M^2) = 273 K / (1 + .2 * .8^2) = 242 K = -31 C

The ISA (international standard atmosphere) temperature at FL 300 is -44 C. So this would be 13 degrees warmer than ISA ("ISA + 13") -- pretty plausible at these latitudes. It also corresponds well with the temperature on the ground: At the field elevation of 7500 feet, ISA temperature is 0 degrees, so the observed temperature of 16 degrees is ISA + 16".

If your aircraft indicates SAT (often labeled OAT) in addition to TAT, you can take a look at the two values and compare them.

[ThomseN_inc 1,128]

3 hours ago, martinboehme said:

I don't think there's anything wrong here. All of these values look plausible.

It's important in this context that TAT (total air temperature) is not the same as the temperature of the free air outside the aircraft -- that would be SAT (static air temperature). When the aircraft is in flight, TAT is higher than SAT; the difference between the two is called ram rise, and it increases with speed. This Wikipedia article contains more details:

https://en.wikipedia.org/wiki/Total_air_temperature

Here are two rules of thumb for calculating TAT for a given SAT and speed (either in knots or Mach number):

TAT = SAT + (TAS / 87)^2

TAT = SAT * (1 + .2 M^2)

(For the second formula, the temperatures need to be in Kelvin.)

For your first scenario, in the initial climb, let's assume SAT is still the same as it was on the ground, and that you have a speed of 250 knots. This gives us:

TAT = 16 C + (250/87)^2 = 24 C

This is in pretty good agreement with your observation.

For the second scenario, let's work backwards from your observed TAT to work out what the SAT is. A TAT of 0 C is 273 K, and I'll assume that you're cruising at Mach 0.8. We get

SAT = TAT / (1 + .2 M^2) = 273 K / (1 + .2 * .8^2) = 242 K = -31 C

The ISA (international standard atmosphere) temperature at FL 300 is -44 C. So this would be 13 degrees warmer than ISA ("ISA + 13") -- pretty plausible at these latitudes. It also corresponds well with the temperature on the ground: At the field elevation of 7500 feet, ISA temperature is 0 degrees, so the observed temperature of 16 degrees is ISA + 16".

If your aircraft indicates SAT (often labeled OAT) in addition to TAT, you can take a look at the two values and compare them.

Totally agree with that. But i am unsure. Why do i observe this only when flying from HAAB. Wouldn't it be the same when flying from a northern europe airport with the same TAT/SAT at groundlevel? Flying in europe i never saw a temperature that high at FL300. The 737 usually takes me to FL370 in about 20 Minutes. Yesterday flying out of Addis it took about 35 minutes. climbing at around 500 ft/min on the last few thousand foot.

[martinboehme 522]

13 minutes ago, ThomseN_inc said:

Why do i observe this only when flying from HAAB. Wouldn't it be the same when flying from a northern europe airport with the same TAT/SAT at groundlevel?

No, because that northern European airport is likely close to sea level, so a SAT of 16 degrees is just ISA + 1. Climb from that airport to 7500 feet (the elevation of HAAB) and you'd expect to see only +1 degree SAT, assuming the standard ISA lapse rate of 2 degrees per 1000 feet.

Put differently, 16 degrees at an elevation of 7500 feet corresponds to 31 degrees at sea level. Those are the equivalent conditions to think about if you're used to flying from sea level airports. The warm temperature relative to ISA explains why you're seeing bad climb performance.

 

Edited November 16, 2023 by martinboehme
Typo

[F737MAX 5,738]

28 minutes ago, ThomseN_inc said:

Wouldn't it be the same when flying from a northern europe airport with the same TAT/SAT at groundlevel?

To follow martinboehme's point, to have the same effect as a northern europe airport at ground level (0 feet MSL) with a TAT of 16°C, the temperature on the ground (7,500 feet MSL) in HAAB would have had to have been just 1°C.

[ThomseN_inc 1,128]

9 minutes ago, F737MAX said:

To follow martinboehme's point, to have the same effect as a northern europe airport at ground level (0 feet MSL) with a TAT of 16°C, the temperature on the ground (7,500 feet MSL) in HAAB would have had to have been just 1°C.

It all makes perfect sense, yes. And thats what i learned. But what i find a bit strange is that the temperature suddenly rises from 16° (in this casre) to about 25° when climbing out. So for example Takeoff at 16° ground level (7500') and at FL150 i was observing 25°. Thats what i was stumbling about.... I know there are inversions and stuff but surely not every day with more or less the same values.

[martinboehme 522]

41 minutes ago, ThomseN_inc said:

It all makes perfect sense, yes. And thats what i learned. But what i find a bit strange is that the temperature suddenly rises from 16° (in this casre) to about 25° when climbing out. So for example Takeoff at 16° ground level (7500') and at FL150 i was observing 25°. Thats what i was stumbling about...

It can be misleading to compare TATs. I'd suggest looking at SAT instead -- I believe on the 737 NG you can find that in the FMC on the PERF (or PROG?) page.

What speed were you doing at FL 150? Assuming you were doing a standard 737 NG climb profile, you'd be doing 280 KIAS. As the formula for ram rise is expressed in terms of TAS, we need to convert IAS to TAS. At FL 150, 280 KIAS corresponds to about 350 KTAS. Plugging that into the formula, we get:

SAT = TAT - (TAS / 87)^2 = 25 - (350 / 87)^2 = 9

I agree that this seems pretty warm for FL 150 (it's ISA+24), but I wouldn't discount it without checking against a real-world source. (I haven't unfortunately been able to find vertical profiles for HAAB.)

41 minutes ago, ThomseN_inc said:

I know there are inversions and stuff but surely not every day with more or less the same values.

Are you saying you're running with real-world weather and nevertheless you're observing the same temperatures every day? That would indeed seem strange, and it's not something I've observed so far.

[JRBarrett 3,121]

The upper air temperatures over HAAB are very high compared to standard (ISA). This is not unusual in that part of Africa. According to the upper wind data in Foreflight, the static air temperature at FL300 over HAAB is -30 C which is 15 degrees C above normal. When you are flying through that airmass at high speed, an equivalent TAT of 0 C is correct. It’s even warmer at FL210 - (ISA +20).

Edited November 16, 2023 by JRBarrett

[martinboehme 522]

13 minutes ago, JRBarrett said:

According to the upper wind data in Foreflight, the static air temperature at FL300 over HAAB is -30 C which is 15 degrees C above normal.

Thanks for that data -- hadn't thought to check ForeFlight (and I'm not sure if my subscription covers Africa). That temperature agrees almost exactly with what I had computed earlier from the TAT.

13 minutes ago, JRBarrett said:

It’s even warmer at FL210 - (ISA +20).

This isn't far off from the ISA + 24 that I computed for FL 150 above. Could you check ForeFlight for the current temperature at FL 150 by any chance?

[ThomseN_inc 1,128]

1 hour ago, martinboehme said:

Are you saying you're running with real-world weather and nevertheless you're observing the same temperatures every day? That would indeed seem strange, and it's not something I've observed so far.

Yes that was my observation over the last days. Not exactly the same values but more or less. And the pattern is always the same. Temperature decreases for a short period of time during climb and suddenly starts to rise as i said above.

Again: I am not saying the sim is faulty. I was just wondering if what i was encountering is a normal thing as i barely flew in africa before and therefore i didn't have any comparison.

[JRBarrett 3,121]

3 hours ago, martinboehme said:

Thanks for that data -- hadn't thought to check ForeFlight (and I'm not sure if my subscription covers Africa). That temperature agrees almost exactly with what I had computed earlier from the TAT.

This isn't far off from the ISA + 24 that I computed for FL 150 above. Could you check ForeFlight for the current temperature at FL 150 by any chance?

SAT right now at FL150 above HAAB is 1C, which is ISA +16

[martinboehme 522]

3 hours ago, JRBarrett said:

SAT right now at FL150 above HAAB is 1C, which is ISA +16

Thanks! That's less consistent then with the value that @ThomseN_inc observed... but then that observation is likely from at least a day ago.

Certainly, the value is in the range of what is plausible.

[JRBarrett 3,121]

8 minutes ago, martinboehme said:

Thanks! That's less consistent then with the value that @ThomseN_inc observed... but then that observation is likely from at least a day ago.

Certainly, the value is in the range of what is plausible.

That’s static air temperature. TAT would be much higher, depending on the airspeed.