Cruise altitude

[ScottG]

Assuming 0 wind and standard temps and pressures how is the altitude that gives maximum speed determined for a jet as well as a turbo prop. Furthermore how is the altitude for maximum range calculated. I know many aircraft vary but I am asking for general consideration, i.e. climb until you can't maintain maximum IAS or hit the mach limit......basically what are the general indications for maximum possible ground speed.

[B767Driver]

Originally Posted by ScottG

Assuming 0 wind and standard temps and pressures how is the altitude that gives maximum speed determined for a jet as well as a turbo prop. Furthermore how is the altitude for maximum range calculated. I know many aircraft vary but I am asking for general consideration, i.e. climb until you can't maintain maximum IAS or hit the mach limit......basically what are the general indications for maximum possible ground speed.

Maximum range will be found at a certain Angle of Attack. In props...it's an AOA that corresponds with L/D max. In a jet, maximum range is found at a slightly different AOA. Since a jet produces thrust, the relationship is a bit different....a speed that corresponds to an AOA that maintains a proportion of the square root on the CsubL to the CsubD. Therefore, in a jet max range is at a slightly faster speed than L/Dmax.

Maximum TAS will be found around FL270. This is also the point where the maximum IAS can be maintained up to a certain Mach number. At this point the air density drops off rapidly causing a reduction in engine thrust output. TAS equals IAS multiplied by the square root of the SL air pressure divided by the actual air pressure at altitude....or simply the pressure ratio.

Flying above FL 270 will not get you there faster...but will save you lots of gas.

[tgrayson]

Originally Posted by ScottG

Assuming 0 wind and standard temps and pressures how is the altitude that gives maximum speed determined for a jet as well as a turbo prop. Furthermore how is the altitude for maximum range calculated. I know many aircraft vary but I am asking for general consideration, i.e. climb until you can't maintain maximum IAS or hit the mach limit......basically what are the general indications for maximum possible ground speed.

Offhand, I'd say that max speed occurs at the highest altitude where the aircaft can maintain max continuous power. Looking at a performance chart for a C172, the highest TAS occurs at 8,000 ft, where the a/c has 80% power available. Without reviewing the literature, I'd say this is true for a jet as well.

For a propeller aircraft, max range is independent of altitude, if you ignore the cost of the climb. As for endurance, it's maximized when fuel flow (FF) is minimized. Since in props, FF is proportional to power, FF is minmized when power is minimized. Since for any given airspeed, it takes more power to fly it the higher you are, lower altitudes are better.

For jets, max range increases with altitude. Max endurance occurs when the fuel flow (FF) is at a minimum. Since FF is roughly proportional to drag in a jet, FF is minimized when drag is minimized, which should be at L/Dmax. Since drag at a particular airspeed does not vary with altitude, and FF is proportional to drag, max endurance will not vary with altitude.

The reason that jets and props are different is mostly due to the powerplant:

1. FF in props is related to the amount of power the engine is producing, but in jets it's related to the thrust.
2. For props, power is roughly constant with airspeed (assuming CS prop), but jets experience increasing power with airspeed
3. For props, thrust decreases with airspeed, but jets (turbojets) have roughly constant thrust with airspeed.

[SteveC]

Originally Posted by tgrayson

For jets, max range increases with altitude. Max endurance occurs when the fuel flow (FF) is at a minimum. Since FF is roughly proportional to drag in a jet, FF is minimized when drag is minimized, which should be at L/Dmax. This will be independent of altitude.

I had to read this paragraph three times to get the gist of the last sentence; "This will be independent of altitude". "This" refers to "FF is minimized...at L/Dmax", not "max range", yes?

[tgrayson]

Originally Posted by SteveC

I had to read this paragraph three times to get the gist of the last sentence; "This will be independent of altitude". "This" refers to "FF is minimized...at L/Dmax", not "max range", yes?

Yes, sorry. It's a big topic to be summarized in a few sentences. Max endurance is altitude independent, since flight at a given IAS (EAS, really) incurs the same drag at all altitudes.

[SteveC]

I think I'm following now. Max endurance is altitude independent, max range is altitude dependent (?).

[tgrayson]

Originally Posted by SteveC

I think I'm following now. Max endurance is altitude independent, max range is altitude dependent (?).

Yes! Maybe I should edit the post?

[NJA_Capt]

Originally Posted by ScottG

.....basically what are the general indications for maximum possible ground speed.

From a layman's point of view, go to the AFM and find the altitude that provides the highest true airspeed for the given weight/temp. For the Citation X, the highest TAS is between FL370-FL410.

http://citationx.cessna.com/performance.chtml

[SteveC]

Originally Posted by tgrayson

Yes! Maybe I should edit the post?

Thanks. The information was all there to begin with, I just don't read so good sometimes.

[staplegun]

Originally Posted by tgrayson

For jets, max range increases with altitude. Max endurance occurs when the fuel flow (FF) is at a minimum. Since FF is roughly proportional to drag in a jet, FF is minimized when drag is minimized, which should be at L/Dmax. Since drag at a particular airspeed does not vary with altitude, and FF is proportional to drag, max endurance will not vary with altitude.

This is not a true statement.



Kevin

[tgrayson]

Originally Posted by staplegun

This is not a true statement.
Kevin

You'll need to elaborate. My statement is in accordance with standard aerodynamic theory.

[ScottG]

Originally Posted by tgrayson

You'll need to elaborate. My statement is in accordance with standard aerodynamic theory.

I didn't think FF was proportional to drag but to density......so higher altitude would mean same drag at a given IAS but lower density=lower FF. I dunno though thats why I ask.

But specifically now I am looking at obtaining max ground speed in a turbine powered airframe......is it as simple as climbing until you can't maintain max IAS(EAS)? Then above that keep climbing until you reach a AOA for max range?

[staplegun]

Originally Posted by tgrayson

You'll need to elaborate. My statement is in accordance with standard aerodynamic theory.

Max endurance in a turbojet does vary with altitude since TSFC decreases as you climb and the temperature goes down, up to the tropopause.


Kevin

[B767Driver]

Originally Posted by NJA_Capt

From a layman's point of view, go to the AFM and find the altitude that provides the highest true airspeed for the given weight/temp. For the Citation X, the highest TAS is between FL370-FL410.

http://citationx.cessna.com/performance.chtml

That TAS would be faster 10,000 feet lower if you had performance numbers for it. Next time you fly...hold a constant IAS/Mach up to cruise altitude and monitor the TAS indicator.

[B767Driver]

Originally Posted by ScottG

But specifically now I am looking at obtaining max ground speed in a turbine powered airframe......is it as simple as climbing until you can't maintain max IAS(EAS)?

Yes, above this altitude density falls faster than temperature. Ultimately, the TAS is derived by the amount of IAS multiplied by the atmospheric density ratio. So, your fastest TAS is also the altitude where you achieve your fastest IAS.

Max IAS will be achieved around FL270.

[B767Driver]

Originally Posted by tgrayson

Since drag at a particular airspeed does not vary with altitude, .[/list]

Are you sure about this?

[tgrayson]

Originally Posted by staplegun

Max endurance in a turbojet does vary with altitude since TSFC decreases as you climb and the temperature goes down, up to the tropopause.

Seems like a valid objection. Still, the standard analysis doesn't take this into account, such as here:

http://selair.selkirk.bc.ca/aerodyna...nce/Page5.html

I'll have to check my other references when I get home.

[tgrayson]

Originally Posted by B767Driver

Are you sure about this?

Well, D = Cd * (1/2 rho V^2) * A, so you have two variables, rho and V. Now V in that equation is TAS; you can replace it with EAS if you replace rho with rho_0, which is sea level density. Then drag will only vary with EAS.

Doesn't take into account any Mach or Reynold's number effects. Since we're talking about relatively low airspeeds, it doesn't seem that it would be too much of an error.

[staplegun]

Originally Posted by tgrayson

Seems like a valid objection. Still, the standard analysis doesn't take this into account, such as here:

http://selair.selkirk.bc.ca/aerodyna...nce/Page5.html

I'll have to check my other references when I get home.

From the same web-site, page 9:

Jet Aircraft

The TSFC of the jet engine improves up to the altitude for the coldest air temperature. In the ISA this is the tropopause. (TSFC holds constant in the stratosphere.)

1. Endurance will increase with altitude as long as temperature decreases with altitude. Maximum endurance will therefore occur at the tropopause.




Kevin

[staplegun]

Originally Posted by tgrayson

Well, D = Cd * (1/2 rho V^2) * A, so you have two variables, rho and V. Now V in that equation is TAS; you can replace it with EAS if you replace rho with rho_0, which is sea level density. Then drag will only vary with EAS.

Doesn't take into account any Mach or Reynold's number effects. Since we're talking about relatively low airspeeds, it doesn't seem that it would be too much of an error.

You stated this:

"Since drag at a particular airspeed does not vary with altitude"

From the website you cited:


"As the aircraft climbs into the less dense air the parasite drag decreases, but the induced drag increases. As a result the total drag curve moves to the right."




Kevin

[tgrayson]

Originally Posted by staplegun

From the same web-site, page 9:1. Endurance will increase with altitude as long as temperature decreases with altitude. Maximum endurance will therefore occur at the tropopause.

Kevin

Interesting. On page 5 he says:

As you can see in the graphs to the left there should be no change in the maximum endurance of the aircraft with altitude.

[B767Driver]

TG,

While it's not my favorite reference read page 172 of Aerodynamics for Naval Aviators. Aerodynamically, the airframe doesn't care what altitude it's at for endurance. But the jet engine's efficiency is much improved and specific fuel consumption is much less at altitude.

I believe that's where the disconnect lies.

[tgrayson]

Originally Posted by staplegun

You stated this:As the aircraft climbs into the less dense air the parasite drag decreases, but the induced drag increases. As a result the total drag curve moves to the right."

That's with respect to TRUE airspeed.

[tgrayson]

Originally Posted by B767Driver

But the jet engine's efficiency and specific fuel consumption is much less at altitude. I believe that's where the disconnect lies.

So it seems, but any analysis of a jet's endurance should have incorporated that data, or the results are meaningless. The author stated "Minimum FF does not change with altitude." That statement doesn't seem compatible with TSFC decreasing with altitude, which he apparently agrees with on another page.

[NJA_Capt]

Originally Posted by B767Driver

That TAS would be faster 10,000 feet lower if you had performance numbers for it. Next time you fly...hold a constant IAS/Mach up to cruise altitude and monitor the TAS indicator.

I don't have a book at home, but I ran it through the FMS software. For a 2 hour flight, the FMS calculates an "optimal" cruise at FL280. Running a "What If" calculation for FL370, the leg time decreases by 1 min and 1000# fuel. For a 3 hour leg it was also 1 min quicker / 2000# less fuel.