Temperature, density altitude, and performance

[birdus]

This is something I'm confused about (almost ready to begin Private Pilot training).

I believe that on a cold day, my plane will perform better—engine, prop, and wing. I thought that was because cold air is more dense. However, now I'm reading that there is higher pressure with warmer air and lower pressure with colder air. Isn't there a direct correlation between density and pressure?

Apparently, the altimeter will read higher than my actual altitude when the air gets colder (Figure 5.15 in the FAA's Weather Circular). Again, I thought I would need to fly higher in cold air to get a given reading because the cold air is denser and so if I flew higher, then I would have less air above me pressing down in the "column" of air.


I think I'm losing my mind.

Thanks,
Jay

 

[dtuuri]

Just think of the weight of a column of air resting on a bathroom scale. That's what the altimeter is measuring — weight. Hot air expands, so the top of the column rises up, but the weight (pressure) stays the same. The column is stratified by pressure levels, so standing on a mountaintop holding an altimeter you'd notice the hands indicating a lower altitude as the temperature increases. When the temp dips, the hands show higher than before and an airplane flying by following a pressure level (constant altitude) will come closer to the mountain than on a warmer day: "High to low or hot to cold, look out below!"

 

[1RTK1]

High pressure fronts can be cold or warm and visa versa for low pressure fronts. Cold air is denser than warm air, as altitude increase temperatures decrease, inversions not withstanding, but pressure also decreases.
High to low look out below goes for both temperature and pressure.
Wish I had the graphic to show it, that would make it easier to understand. Should be in the pilots aeronautical handbook free from the faa.

 

[Sport Pilot]

 

[alfadog]

...

Isn't there a direct correlation between density and pressure?

...

Yes, it is the ideal gas law: PV = nRT

edit: You can work that around to show the direct correlation: p (or P) = RrT where R is a constant and r is density.
That tells us that, for a given pressure, temperature (in Kelvin) and density are inversely proportional.

 

[alfadog]

And to your point, the same column of air (barometric pressure) than be more dense or less dense at any given altitude. I would think.

 

[Salty]

Just think of the weight of a column of air resting on a bathroom scale. That's what the altimeter is measuring — weight. Hot air expands, so the top of the column rises up, but the weight (pressure) stays the same. The column is stratified by pressure levels, so standing on a mountaintop holding an altimeter you'd notice the hands indicating a lower altitude as the temperature increases. When the temp dips, the hands show higher than before and an airplane flying by following a pressure level (constant altitude) will come closer to the mountain than on a warmer day: "High to low or hot to cold, look out below!"

I think I've finally figured out a way to make sense of this. Following is a few randomish statements that help me work this out.

At sea level the altimeter won't change with the temperature because the weight of the air above sea level isn't changing.
On top of the mountain (or up in an airplane) it will change, because denser air means less of it is above you (less weight above you)
To extend the previous two statements, the higher you are the larger the error from this effect. This is shown in the pictures above in that the lines are less steep when lower.
Putting an altimeter in the freezer when on top of the mountain won't change it's reading because it's not the temperature of the air it's reading that matters, it's the change in configuration of the column of air that it's in that matters, and putting in a freezer isn't changing that.


And it's that last statement that is the root of my confusion. I want to use the air being sampled to explain the error, and you simply can't. You have to look at the bigger picture of the atmosphere and how the temperature effects it. Temperature isn't effecting the altimeter at all, it's changing the atmosphere in a way that makes the altimeter inaccurate.

 

[birdus]

I think I've finally figured out a way to make sense of this. Following is a few randomish statements that help me work this out.

At sea level the altimeter won't change with the temperature because the weight of the air above sea level isn't changing.
On top of the mountain (or up in an airplane) it will change, because denser air means less of it is above you (less weight above you)
To extend the previous two statements, the higher you are the larger the error from this effect. This is shown in the pictures above in that the lines are less steep when lower.
Putting an altimeter in the freezer when on top of the mountain won't change it's reading because it's not the temperature of the air it's reading that matters, it's the temperature of the column of air that it's in that matters.

And it's that last statement that is the root of my confusion. I want to use the air being sampled to explain the error, and you simply can't. You have to look at the bigger picture of the atmosphere and how the temperature effects it. Temperature isn't effecting the altimeter at all, it's changing the atmosphere in a way that makes the altimeter inaccurate.

Truthfully, I'm still mulling this over and not completely getting it, so I appreciate the additional thoughts. I hate the idea of using mnemonics to "understand" things. I actually like to understand what's going on, so I'll keep working on it.

Thanks,
Jay

 

[Salty]

Truthfully, I'm still mulling this over and not completely getting it, so I appreciate the additional thoughts. I hate the idea of using mnemonics to "understand" things. I actually like to understand what's going on, so I'll keep working on it.

Thanks,
Jay

I've spent the last 5 years trying to figure out a way to actually understand and explain it rather than using rote memory. This is the closest I've gotten so far.

The pressure in the air is actually changing. That's the key. Because the air is becoming more dense, it's sinking and there's less above you so there's less pressure where you are. But the pressure on the ground is still the same because all the air is above the ground (at sea level). So the altimeter setting is correct, but only when at sea level.

Maybe another way to look at it is that temperature effects the rate of pressure change as altitude changes. When it's cold, the pressure goes down faster as you climb than it does when it's hot.

My mind wants to conflate pressure and density and say the air is more dense, so there's more pressure, but that's just plain wrong.

 

[birdus]

Because the air is becoming more dense, it's sinking and there's less above you so there's less pressure where you are.

My mind wants to conflate pressure and density and say the air is more dense, so there's more pressure, but that's just plain wrong.

You just made my head explode. This is precisely a point which has confused me. Gonna have to mull this over.

One thing that seems odd to me is the idea that the vacuum of space could begin at different altitudes, i.e., that the "top" of the atmosphere can rise and lower based on its density. I suppose there's no reason it couldn't, though, since gravity varies over the surface of the Earth, so that altitude could vary even if there were the same density everywhere. I just need to get used to that idea.

Thanks,
Jay

 

[WDD]

The pressure at sea level does go up and down as well. 29.92 is the standard pressure at standard temperature (15 C) at sea level, but temperatures do change, low and high pressure systems also occur at sea level, etc.

Yes, cold air is more dense.

But - air pressure is not air density.

Low pressure areas form when atmospheric circulations of air up and down remove a small amount of atmosphere from a region. This usually happens along the boundary between warm and cold air masses by air flows "trying" to reduce that temperature contrast.

Cold air results in change in up and down circulation, leads to the top of the air mass you're under going somewhere else, resulting in less air being on top of you, resulting in less air pressure.

So the bubble of air on top of you is colder, more dense, but less of it, so less weight of air pushing down on you.

 

[Salty]

You just made my head explode. This is precisely a point which has confused me. Gonna have to mull this over.

One thing that seems odd to me is the idea that the vacuum of space could begin at different altitudes, i.e., that the "top" of the atmosphere can rise and lower based on its density. I suppose there's no reason it couldn't, though, since gravity varies over the surface of the Earth, so that altitude could vary even if there were the same density everywhere. I just need to get used to that idea.

Thanks,
Jay

A high pressure area is nothing but the atmosphere being "taller" in that area. A hurricane is where the air spills into a very small, low pressure area (an area where the atmosphere is very shallow).

 

[Salty]

The pressure at sea level does go up and down as well. 29.92 is the standard pressure at standard temperature (15 C) at sea level, but temperatures do change, low and high pressure systems also occur at sea level, etc.

I need to understand this. I don't understand how. What causes a pressure change at sea level when the temperature changes?

 

[WDD]

The amount of air above the earth isn't a nice smooth layer. Think of a pond with waves, etc. Or bubbles / foam in a sink - a bit bumpy.

 

[birdus]

A high pressure area is nothing but the atmosphere being "taller" in that area.

Why would it have to be taller? Couldn't it just be denser? That would make pressure higher at my location.

 

[WDD]

Pressure changes at sea level not so much because of temperature change, but because hot air signifies that there is a higher pressure system in the weather than a weather system that could be cooler next to it. Colder air - top of air mass moves somewhere else, less air on top of you. Hotter air - you have more air. (Hey, this is what I've landed on. Always looking to learn more. It isn't intuitive IHMO).

 

[WDD]

Why would it have to be taller? Couldn't it just be denser? That would make pressure higher at my location.

Taller = more air on top of you. Dirt is less dense than sand. Which is heavier? 100 miles of dirt or 75 miles of sand? A lot more of the slightly less dense stuff weighs more than less of the dense stuff.

 

[birdus]

Taller = more air on top of you. Dirt is less dense than sand. Which is heavier? 100 miles of dirt or 75 miles of sand? A lot more of the slightly less dense stuff weighs more than less of the dense stuff.

Clear as mud, or dirt, or sand.

 

[FlightInsight]

The altimeter measures the pressure placed on it by air molecules above it. We calibrate the altimeter by telling it what the sea level atmospheric pressure is at a nearby station. As temperatures increase and decrease, the air molecules above us expand and contract, but since the total number of molecules is the same, pressure is the same.

When we're at sea level, this isn't a problem, but up at altitude, the expanded or contracted "column" of air confuses the altimeter. We've only told it about sea level pressure, so it makes an assumption about the density of air molecules at higher altitudes - this is the Standard Atmosphere model. When actual outside air temperatures are different than standard, the altimeter will read incorrectly.

The higher up we fly, the greater these non standard temperature errors become, until finally, we give up above 18,000 feet, and just call our altitude a "Flight Level."

You can test this out if you live in a high altitude area like Denver: First set an altimeter to sea level pressure at a time of day when temps are close to standard. Then come back when the temps are higher or lower than standard, and reset to sea level pressure. At a true altitude of 7,000 feet, a drop of 15°C will cause the altimeter to ready 400 feet higher.

Dan, CFI

 

[WDD]

Air pressure at sea level does change however. A hurricane passes over you. Pressures will change! Extreme example, but shows the point.

 

[Salty]

Air pressure at sea level does change however. A hurricane passes over you. Pressures will change! Extreme example, but shows the point.

That’s not due to temperature though

 

[FlightInsight]

I've just uploaded a video that explains this concept. To show how temperature affects the altimeter, I put mine in the freezer and in the oven!

Enjoy!

Dan, CFI

 

[Salty]

I've just uploaded a video that explains this concept. To show how temperature affects the altimeter, I put mine in the freezer and in the oven!

Enjoy!

Dan, CFI

You highlight another thing that throws me. Temp does effect the altimeter because the internal diaphragm will expand and contract due to density changes, but in the opposite way the faa question wants you to answer.

 

[dtuuri]

Maybe it helps to have a sketch in mind for these questions. Here, you can borrow mine:

​

 

[LongRoadBob]

I've just uploaded a video that explains this concept. To show how temperature affects the altimeter, I put mine in the freezer and in the oven!

Enjoy!

Dan, CFI

I’m missing something. When you at home went high to low temp, the altimeter went from showing 60’ to 40’.
So assuming your house is flying straight and level, didn’t it go the wrong way?
If your house were flying, and you used the altimeter to keep it at 60’ you would start seeing the altitude drop, as temp went down, so you’d climb and have your house actually be at 80’ while it read 60’ right?
so where is the “look out below”? altimeter showing 60’ as it got colder means you are higher, not lower?

it’s morning here, I just woke up. I expect I’m thinking about this wrong. But I expected the altimeter to read higher when cold.

 

[Salty]

I’m missing something. When you at home went high to low temp, the altimeter went from showing 60’ to 40’.
So assuming your house is flying straight and level, didn’t it go the wrong way?
If your house were flying, and you used the altimeter to keep it at 60’ you would start seeing the altitude drop, as temp went down, so you’d climb and have your house actually be at 80’ while it read 60’ right?
so where is the “look out below”? altimeter showing 60’ as it got colder means you are higher, not lower?

it’s morning here, I just woke up. I expect I’m thinking about this wrong. But I expected the altimeter to read higher when cold.

This is the confusing part. The altimeter error is the other way, but it’s very small. The atmospheric error is “high to low look out below” and is larger. Watch it again.

 

[Lachlan]

I’m missing something. When you at home went high to low temp, the altimeter went from showing 60’ to 40’.
So assuming your house is flying straight and level, didn’t it go the wrong way?
If your house were flying, and you used the altimeter to keep it at 60’ you would start seeing the altitude drop, as temp went down, so you’d climb and have your house actually be at 80’ while it read 60’ right?
so where is the “look out below”? altimeter showing 60’ as it got colder means you are higher, not lower?

it’s morning here, I just woke up. I expect I’m thinking about this wrong. But I expected the altimeter to read higher when cold.

That was the temperature error. His house, and freezer, were at the same atmospheric pressure for the duration of the test.

 

[dtuuri]

I’m missing something. When you at home went high to low temp, the altimeter went from showing 60’ to 40’.
So assuming your house is flying straight and level, didn’t it go the wrong way?
If your house were flying, and you used the altimeter to keep it at 60’ you would start seeing the altitude drop, as temp went down, so you’d climb and have your house actually be at 80’ while it read 60’ right?
so where is the “look out below”? altimeter showing 60’ as it got colder means you are higher, not lower?

it’s morning here, I just woke up. I expect I’m thinking about this wrong. But I expected the altimeter to read higher when cold.

I don't know what freezing an altimeter in the kitchen has to do with the reason it reads erroneously when following a pressure level through the sky. That video lost me completely and I know this subject well. Under the same temperature stratification the pressure levels are parallel. If not the same, they aren't (see the figures several posts up thread). Your altimeter follows the pressure level, which is the result of the weight of the sky above it to the top of the atmosphere.

 

[Southpaw]

Boy this makes my head ache. As a student pilot I understand the need to know and be able to figure it out but ...
I have a bowling ball Mortar. 4 Ounces of FG Black Powder will move a 15 lb bowling ball 800 Yards on a cool Crisp October day .
4th of July @ 80 degrees its lucky to reach 700 yards.
This tells me cool air allows more "lift" than hot air ?
My dad flew a rented Cherokee 140 up to Canada to pick up some cultivator parts . His weight and balance was ok . Just him 2 cultivator shanks and clamps on board. Taking off from Taber,Alberta heading west on a hot day it took him 10 miles to get enough altitude before he felt comfortable to make a turn heading south. The runway was all gone when he lifted off. He didn't do a density altitude calculation. Doubt in his years of flying from 1946 to the early 80's that he ever did .

 

[birdus]

I have a bowling ball Mortar. 4 Ounces of FG Black Powder will move a 15 lb bowling ball 800 Yards on a cool Crisp October day . 4th of July @ 80 degrees its lucky to reach 700 yards. This tells me cool air allows more "lift" than hot air ?

Cool! I would love to see your big gun in action! I'm guessing it goes farther on the cool day because of the denser air (i.e., more oxygen) burning in the chamber/barrel rather than "lift."

 

[Southpaw]

Cool! I would love to see your big gun in action! I'm guessing it goes farther on the cool day because of the denser air (i.e., more oxygen) burning in the chamber/barrel rather than "lift."

I need to find the video file and upload it to my online provider.

 

[John Myers]

I struggled with this also. The thing that helped was considering a balloon that is inflated and comparing it to a steel tank. Assume you inflate a balloon to some pressure. If you increase the temperature in the balloon, the pressure remains about the same because the balloon expands with the increased energy and velocity of the molecules of air within it.

Now consider the same with a SCUBA tank. If you heat it, the pressure will also increase because the volume of the tank is fixed. The atmosphere is more like the balloon than the SCUBA tank.

If you have a WAAS GPS you can reference that altitude and compare to your altimeter. It is usually more accurate (but should not be used to maintain the altitude ATC gives you). Once you get this figured out, look at why indicated airspeed drops with constant thrust and decreasing air density...

Incidentally, oxygen requirements are physiologically based on pressure altitude, not true or density altitude, because the pressure is what is relevant in determining how easily oxygen can pass into your blood.

 

[dtuuri]

I struggled with this also. ...

Once you get this figured out, look at why indicated airspeed drops with constant thrust and decreasing air density...

Indicated airspeed (IAS) doesn't drop with constant thrust, AFAIK. IAS is proportional to drag, so for a "constant thrust" you must have constant drag, if we're talking about uniform flight without acceleration, either positive or negative. A lessening of air density would reduce drag and the "constant thrust" would accelerate back to uniform flight at the previous IAS, albeit at a higher true airspeed (TAS). IMO. One of us will have more struggling in store, I'm afraid. Perhaps you meant "power" not thrust?

 

[John Myers]

Indicated airspeed (IAS) doesn't drop with constant thrust, AFAIK. IAS is proportional to drag, so for a "constant thrust" you must have constant drag, if we're talking about uniform flight without acceleration, either positive or negative. A lessening of air density would reduce drag and the "constant thrust" would accelerate back to uniform flight at the previous IAS, albeit at a higher true airspeed (TAS). IMO. One of us will have more struggling in store, I'm afraid. Perhaps you meant "power" not thrust?

Well, maybe I still don't understand it. I won't hijack the thread but there is another on the forum about this.

 

[RonP]

I understand the performance is better for engine, prop and wing in colder denser air. What has always had me curious about this is why air races and speed runs are made in hot climates such as Nevada. If colder denser air improves the 3 items listed why don’t air races and speed runs be made in colder climates?

 

[John Myers]

I understand the performance is better for engine, prop and wing in colder denser air. What has always had me curious about this is why air races and speed runs are made in hot climates such as Nevada. If colder denser air improves the 3 items listed why don’t air races and speed runs be made in colder climates?

Denser air requires more work to move through, so it's not better if by better you mean faster.

 

[RonP]

To go fast you need to increase engine performance, prop performance and wing performance. Compared to less dense air doesn’t that decrease engine performance, prop performance and wing performance? Certainly drag goes down in less dense air but so does the performance of the engine developing less power and less bite on the prop plus more wing area to support it all. Could it be the drag coefficient is the critical factor with reduced engine and prop performance in less dense air? If so than on a hot day my speed and gph is better than on a cold day.

 

[John Myers]

To go fast you need to increase engine performance, prop performance and wing performance. Compared to less dense air doesn’t that decrease engine performance, prop performance and wing performance? Certainly drag goes down in less dense air but so does the performance of the engine developing less power and less bite on the prop plus more wing area to support it all. Could it be the drag coefficient is the critical factor with reduced engine and prop performance in less dense air? If so than on a hot day my speed and gph is better than on a cold day.

Engines don’t always develop less power in thinner air. Turbocharged engines aren’t affected much, nor are non turboed engines below about 7000 ft (at cruise power settings). Turbine engines actually generate more thrust at higher altitudes.

Propeller pitch can be increased to maintain thrust. AOA of the wing increases and induced drag increases but parasitic drag is a much larger factor and decreases.

 

[Shuswap BC]

If the mixture is properly leaned a naturally aspirated engine will lose around 3% power per 1000' in elevation above asl. If you don't correct the mixture it can be substantially more than that.

I live in a very mountainous region, and have snowmobiled for a long time. With fuel injection its not as bad now as the old days, but the power loss is still drastic as we climb while mountain riding.

 

[Domenick]

Cool! I would love to see your big gun in action! I'm guessing it goes farther on the cool day because of the denser air (i.e., more oxygen) burning in the chamber/barrel rather than "lift."

https://www.youtube.com/results?search_query=bowling+ball+mortar