Calculating Aircraft Speed: Weight vs Thrust

[treborly45]

How do you figure out how fast an aircraft can travel, in Km/H ,if given the weight and the thrust.

For example: the aircraft weighs 3,100 lbs and has 20,000lbs of thrust

i thought it was 20,000/3,100= 6.5m/s/s which would be 23km/h ?

but a 747 weighs around 850,00 lbs and has 124,000lbs of thrust, but is able to cruise at 910km/h.

So how do you do it?

thanks guys.

 

[mgb_phys]

It's not as simple as that the thrust must overcome the air resistance (drag). To work this out you have to study the aerodynamics, which for something as complex in shape as an aeroplane can only be worked out experimentally in a wind tunnel or simulated on a computer.

I suppose the thrust/weight relationship would be true for an aeroplane going vertically upward with no atmosphere.

 

[Loren Booda]

You might be able to do a rough calculation using the appropriate Reynolds number. See http://en.wikipedia.org/wiki/Reynolds_number.

 

[rcgldr]

Reynolds number doesn't help with the drag factor. Plus the reality is that most commercial aircraft can't go full throttle without exceeding the maximum safe air speed for the structure of the air frame. The 747 is one of the fastest sub-sonic commercial aircraft, able to run at about mach .85 to mach .90 at high altitudes.

 

[AlephZero]

For example: the aircraft weighs 3,100 lbs and has 20,000lbs of thrust

i thought it was 20,000/3,100= 6.5m/s/s which would be 23km/h ?

You seem to be trying to calculate "force = mass * acceleration" (except you have the units mixed up), but trying to convert an acceleration into a velocity is wrong.

In cruise at constant speed, the relevant equations are

thrust force = drag force
weight = lift force

But there's no easy way to calculate the drag force accurately. Even the aircraft designers sometimes get surprises when flight testing starts.

but a 747 weighs around 850,00 lbs and has 124,000lbs of thrust, but is able to cruise at 910km/h.

The max takeoff thrust of a 747 is about 200,000lb to 250,000lb depending on the engine choice. The cruise thrust is nearer 40,000 lb than 124,000lb.

 

[russ_watters]

The limiting factor on an airliner isn't thrust, weight, or drag, it is the speed of sound. As the airliner gets close to the speed of sound, the speed of the air over the wings exceeds the speed of sound and shock waves start to form. The maximum speed of the aircraft is just below that.

 

[rcgldr]

The limiting factor on an airliner isn't thrust, weight, or drag, it is the speed of sound.

For most aircraft, including commercial, speed of sound isn't an issue, it's the drag force and turblence (flutter) on the wings.

From Wiki:

The VNE , or the never exceed speed, of an aircraft is the V speed which refers to the velocity that should never be exceeded due to risk of structural failure, due to calculated factors such as wing or tail deformation or due to aeroelastic 'flutter' (unstable airframe or control oscillation). VNE is specified as a red line on many airspeed indicators. This speed is specific to the aircraft model, and represents the edge of its performance envelope in terms of speed. Well below the speed of sound, the VNE is read as Indicated Air Speed (IAS), since the pitot indication is a direct measure of the dynamic pressure for any given airspeed. At altitude, where TAS is higher than IAS, aerodynamic damping is weaker than at lower levels (damping is proportional to IAS) whereas inertia-induced disturbances are stronger (inertia grows with acceleration, which is the time derivative of TAS). This condition, if continued beyond tested limits, pre-disposes to unstable oscillations or 'flutter'. For instance, the TAS/IAS ratio at 40,000 ft on the ICAO ISA is 2:1, that is, TAS is approximately twice IAS.

http://en.wikipedia.org/wiki/Vno

MMO (Maximum Operating speed) is included in this table of comercial aircraft:

http://www.airnorthwest.net/hubs/klax/performance.html

The Cessna Citation X is unusual in that it's MMO is Mach .92, the same as some 747 (although the Cessna's true air speed is less since it's MMO is rated at a lower altitude).

 

[russ_watters]

There is a difference depending on the altitude. I didn't realize the Vne is so low on such aircraft, but since the speed of sound is below the Vne when the aircraft is at high altitude, the plane's ability to get close to the speed of sound becomes the limiting factor. That's the reason for including an Mmo on the table.

Cessna's info page on the Citation states that the wing is swept more than any other business jet. What it doesn't say is the reason why: it allows the plane to fly faster without shock waves starting to form on the wings.

 

[AlephZero]

For most aircraft, including commercial, speed of sound isn't an issue, it's the drag force and turblence (flutter) on the wings.

But the two effects are highly correlated (except in small aircraft with VNE 200 knots or less), because of the changes in airflow patterns as the speed approaches the speed of sound and the formation of shock waves.

Concorde needed military style jet engines with afterburners to give enough thrust to get through Mach 1, though the cruise speed was just over Mach 2.

 

[Loren Booda]

The speed of sound is different at different areas on the aircraft.

 

[rcgldr]

For most aircraft, including commercial, speed of sound isn't an issue, it's the drag force and turblence (flutter) on the wings.

But the two effects are highly correlated (except in small aircraft with VNE 200 knots or less).

I was including those small aircraft as well in my general statement. Some of the slower speeds listed on that table are around mach .5, where speed of sound isn't a big factor. I'm not so sure that at high altitudes, with MMO's of .82 or less, that speed of sound is the issue versus flutter issues (control surfaces or the wings themselves).

Although the general issue is turbulence for aircraft speed with higher MMO's, the speed of sound and shockwaves are a contributor to the turbulence.

It's also a pretty narrow margin, I recall some crash of a 737 (maybe 707), where the instruments failed at night, and the pilots eventually rolled the plane over on it's side where it picked up speed. Both wings sheered off at about mach .9, only .08 mach above MMO and below the MMO for a 747. At the time, there was a lot of coverage of this, including simulations.

Concorde

This is one of many super-cruise aircraft that can fly supersonic without afterburners, but it does need them until Mach 1.7, and it's more efficient to stay on afterburners while accelerating to Mach 2.0 before shutting them off.

http://en.wikipedia.org/wiki/Concorde

 

[AlephZero]

I was including those small aircraft as well in my general statement. Some of the slower speeds listed on that table are around mach .5, where speed of sound isn't a big factor.

I didn't read every line of the table carefully, but the Mach 0.5 limit typically applies to propellor aircraft, because of the limitation of the prop (i.e. supersonic flow over the blade tips is not efficient). If the propulsion system limits the max speed in level flight, there is no point in designing an passenger carrying airframe that could go a lot faster in a dive without structural failure, at the expense of extra weight. (For aerobatic prop-powered aircraft, this doesn't apply of course). The same basic logic explains why a "spam can" with a cruise speed of say 130kt has a VNE of say 180kt. Putting it another way, 180kt is the limit between "recovery from unusual attitude" and "crash".

I'm not so sure that at high altitudes, with MMO's of .82 or less, that speed of sound is the issue versus flutter issues (control surfaces or the wings themselves).

High bypass ratio turbofans are limited to subsonic speeds for the same basic reason as props - supersonic airflow over the fan blade tips creates big design problems. Also the high drag on a large diameter engine as speed increases.

Supersonic engines need a completely different type of inlet design (often with variable geometry at different speeds) to handle these issues.

It's also a pretty narrow margin, I recall some crash of a 737 (maybe 707), where the instruments failed at night, and the pilots eventually rolled the plane over on it's side where it picked up speed. Both wings sheered off at about mach .9, only .08 mach above MMO

If you want to design a lightweight structure to operate at certain conditions, the safety margin that gives the lightest weight is 1.0, though obviously you can't achieve that. But even for low-speed airflow, aerodynamic loads are usually proportional to velocity squared. That alone means the wing loading at Mach 0.9 is 20% higher than at Mach 0.82. Add onto that compressibility effects and local transonic flow, and exceeding the typical design safety margin of 1.3 seems quite plausible. In other words, the wings probably fell off because they were designed properly, not because they were designed wrong.

 

[treborly45]

So there's no way to even find an approximate speed given those variables?


lets say the aircraft had no wings, it was shaped like a cone.

12 foot in dia, 24 feet long.
its traveling horizontally at 10,000 feet.
its mass is 3,100lbs
there is 3,100lbs of lift and 20,000lbs of thrust acting on it.

can i get an approximate acceleration and a speed in km/h?

 

[F for Freedom]

So there's no way to even find an approximate speed given those variables?


lets say the aircraft had no wings, it was shaped like a cone.

12 foot in dia, 24 feet long.
its traveling horizontally at 10,000 feet.
its mass is 3,100lbs
there is 3,100lbs of lift and 20,000lbs of thrust acting on it.

can i get an approximate acceleration and a speed in km/h?

Well you could use F = ma to find acceleration like you did earlier.

Once you have acceleration you could use one of the kinematic equations to help you find the speed. However, if there is acceleration, you need a bit more information, like the time it is accelerating for, or the distance over which the aircraft accelerates.

 

[mgb_phys]

lets say the aircraft had no wings, it was shaped like a cone.

One of those physicist "assuming a spherical horse running in a vacuum" type answers!