Determining the acceleration of an aircraft

In summary, the individual is seeking help with their research on aircraft performance for a school project. They have used the NASA FoilSim to determine an airfoil profile with a maximum coefficient of lift of 1.888 and have calculated the minimum speed required for lift. They now need to calculate the minimum runway distance for take-off and are looking for ways to reduce this distance while maintaining a final velocity of 39.18 m/s. They also have some requirements for their aircraft, including a maximum take-off weight of 4000 kg and specific take-off and landing speeds. The discussion also touches on the importance of engine thrust in take-off and the relationship between weight, lift, and thrust.
  • #1
GeForce7
7
0
Hello everyone. I'm currently doing a research on aircraft performance for my school project, which require me to design an airfoil to suit a specific mission. I'm not very familiar with the formulas used for calculating the aircraft performance and I would like to seek help from the forum.

Using the NASA FoilSim, I came out with an airfoil profile with a maximum coefficient of lift of 1.888. Using the lift equation, I calculated the minimum speed which I must fulfill in order to gain enough lift to counter the weight which is approximately 39.18 m/s.

V_stall=√(W/(CL_max×0.5×ρ×S))
V_stall=√(39240/(1.888×0.5×1.225×22.1))
V_stall=√(1535.425122)
V_stall=39.18 m∕s or 141.10 km/h
Assuming that the runway distance is 1800 m, how do I calculate the minimum runway distance in order for the aircraft to take-off? What can I do to reduce the distance needed to take-off while keeping the final velocity at 39.18 m/s? Is there a way to increase the acceleration of the aircraft while keeping the same final velocity?

Here are some requirements that my aircraft must fulfill:

  1. Maximum take-off weight of 4000 kg (39240 N)​
  2. Take-off must take place at 1.25 times the stall speed, but less than 200 km/h​
  3. Landing must take place at 1.3 times the stall speed, but less than 180 km/h​
  4. Aircraft must take-off and land at a runway with a distance of 1800 m or less​
 
Engineering news on Phys.org
  • #2
GeForce7 said:
Hello everyone. I'm currently doing a research on aircraft performance for my school project, which require me to design an airfoil to suit a specific mission. I'm not very familiar with the formulas used for calculating the aircraft performance and I would like to seek help from the forum.

Using the NASA FoilSim, I came out with an airfoil profile with a maximum coefficient of lift of 1.888. Using the lift equation, I calculated the minimum speed which I must fulfill in order to gain enough lift to counter the weight which is approximately 39.18 m/s.

V_stall=√(W/(CL_max×0.5×ρ×S))
V_stall=√(39240/(1.888×0.5×1.225×22.1))
V_stall=√(1535.425122)
V_stall=39.18 m∕s or 141.10 km/h
Assuming that the runway distance is 1800 m, how do I calculate the minimum runway distance in order for the aircraft to take-off? What can I do to reduce the distance needed to take-off while keeping the final velocity at 39.18 m/s? Is there a way to increase the acceleration of the aircraft while keeping the same final velocity?

Here are some requirements that my aircraft must fulfill:

  1. Maximum take-off weight of 4000 kg (39240 N)​
  2. Take-off must take place at 1.25 times the stall speed, but less than 200 km/h​
  3. Landing must take place at 1.3 times the stall speed, but less than 180 km/h​
  4. Aircraft must take-off and land at a runway with a distance of 1800 m or less​
You're missing some key components of aircraft performance to make an intelligent study.

Chiefly, what sort of power or thrust can your aircraft's engines produce? Are they recips w/propellers, turboprops, turbojets, ramjets, what?

You can make a barn door fly if you attach enough power to it.

Aircraft performance is dependent on much more than just picking an airfoil for the wing.

Here is a bizjet which has roughly your max. TO weight:

https://en.wikipedia.org/wiki/Cessna_Citation_Mustang
 
  • #3
Thank you for the reply. Let's say my aircraft can produce a maximum take-off thrust of 14000 N, how can I work out the calculation? Can I use the F=ma formula to work out the acceleration? Do pilots always go for maximum engine thrust during take-off?
 
  • #4
GeForce7 said:
Thank you for the reply. Let's say my aircraft can produce a maximum take-off thrust of 14000 N, how can I work out the calculation? Can I use the F=ma formula to work out the acceleration?

You pretty much have to. Of course, F is not just the thrust, it's Fnet, which includes the rolling friction on the landing gear, and the drag on the plane as it increases speed during the takeoff roll, all acting against the thrust of the engines.

Do pilots always go for maximum engine thrust during take-off?
That's what it's there for.

The aircraft on take-off typically has a max load: full fuel, full passengers, full cargo, whatever.

Say the airfield is at a higher elevation; there's no wind blowing down the runway; the air temperature is high, so the air density at altitude is relatively low; you have a short runway with height obstructions just beyond the end of the field. This is the time to crank the throttles wide open, cross your fingers, and hope that your take-off calculations are right, and that you don't have an engine malfunction halfway down the runway.

Once the aircraft is off the ground and flying, the engines are required only to produce enough thrust to counter the drag of the aircraft as it is flying at the set cruising speed and altitude.
 
  • #5
You can both increase acceleration and reduce take off distance by reducing weight. (I don't know if your assignment permits that.) Another way to reduce take off distance is increase maximum lift coefficient or wing area. But in any case you want to plug the total lift of the airplane into your formulae, which is normally wing lift minus stabilizer download, assuming a relatively conventional configuration.

Bear in mind that lift and weight are equal and opposite only in level flight. Climbing or descending, weight is equal and opposite to the vector sum of total aerodynamic force and thrust.
 
Last edited:
  • #6
Thanks you guys for providing me the assistance. Right now, I need to calculate the thrust that can a turbofan engine can produce using F=ma equation. However, I'm not sure how I can approach it. Can I use a hypothetical thrust value and work out the calculation backward? For example, if my maximum take-off thrust is 14,000 N, how do I calculate the mass of the air and acceleration?
 
  • #7
GeForce7 said:
Thanks you guys for providing me the assistance. Right now, I need to calculate the thrust that can a turbofan engine can produce using F=ma equation. However, I'm not sure how I can approach it. Can I use a hypothetical thrust value and work out the calculation backward? For example, if my maximum take-off thrust is 14,000 N, how do I calculate the mass of the air and acceleration?
It's not clear what you want to do here.

Are you trying to figure out how fast an aircraft can move with a set max. thrust, or are you trying to design an engine to give a max. thrust value?

If the latter, it will take much more than F = ma to figure the performance of a turbofan engine.

https://www.grc.nasa.gov/www/k-12/airplane/turbfan.html
 
  • #8
You are correct. I'm trying to figure out an engine that can give me a maximum thrust value of 14,000 N. The formula from NASA's website is too difficult for me to figure it out myself. The thrust value is taken from Pratt and Whitney PW615F which is capable of generating a maximum take-off thrust of 6000 N. Since I'm clueless on the engine thrust calculation, I can only use the thrust value of an engine and pluck it into an equation to calculate the acceleration of my aircraft which is 1.49 m/s^2. In theory, my aircraft can lift off easily and only require a runway distance of 850.05 m which is significantly lesser than requirement. My only issue now is that I need to show the lecturer that the engine thrust value can be calculated.
 
  • #9
GeForce7 said:
You are correct. I'm trying to figure out an engine that can give me a maximum thrust value of 14,000 N. The formula from NASA's website is too difficult for me to figure it out myself. The thrust value is taken from Pratt and Whitney PW615F which is capable of generating a maximum take-off thrust of 6000 N. Since I'm clueless on the engine thrust calculation, I can only use the thrust value of an engine and pluck it into an equation to calculate the acceleration of my aircraft which is 1.49 m/s^2. In theory, my aircraft can lift off easily and only require a runway distance of 850.05 m which is significantly lesser than requirement. My only issue now is that I need to show the lecturer that the engine thrust value can be calculated.
P & W make more than one model of jet engine. There are other engine manufacturers out there, like GE, Rolls-Royce, etc. A thrust of 14000 N is about 3100 lbf, so maybe one of the makers of smaller engines, like Garrett or Williams, would be more what you are looking for. A Williams FJ44-4 is rated at 16000 N.

http://www.williams-int.com/products/fj44-4

Most of these performance data, like static thrust, fuel consumption, etc., are taken not from calculations, but actual engine tests after the design is finished.
 
  • #10
Ok. I will try to convince them that the engine thrust calculation is not feasible and I should just use the thrust value given by the manufacturer for better accuracy.
 
  • #11
GeForce7 said:
Do pilots always go for maximum engine thrust during take-off?

It's pretty rare for them to use max thrust at takeoff actually - they calculate thrust required based on runway length, air density, takeoff weight, and whether or not there are any obstacles to clear (like a large hill or building just past the end of the runway), and then base their takeoff thrust on that. Full thrust is rarely used because it increases engine wear.
 
  • #12
You can calculate thrust using F=ma if you know engine power and the diameter of the engine's ideal (Rankine) actuator disk.
 
  • #13
David Lewis said:
You can calculate thrust using F=ma if you know engine power and the diameter of the engine's ideal (Rankine) actuator disk.

Jet engines don't have a fixed power though (nor do they have a fixed thrust, though that's often a simplifying assumption that's made with them). It's rather complicated to actually get a decent estimate of the thrust of a jet engine.
 
  • #14
Good point. Thrust varies depending on speed even at a fixed throttle setting. At the beginning of the take off run, you have static thrust, but as the airplane picks up speed, thrust changes.

I believe the relationship between thrust and power is:
power = sq rt [(thrust cubed) divided by (2 * air density * area of actuator disk)]
 
  • #15
What kind of power are you trying to get? Power applied to the air? Power applied to the aircraft? The first is rather complicated for jet engines, as the core air has a pretty significant amount of power added in the form of heat, while the bypass air is pretty much just passing through a ducted fan. The second one is easy (but largely useless), as it will simply be the thrust multiplied by the aircraft velocity. I don't see how your formulation could be correct for any definition though - there should definitely be a velocity dependence somewhere in there..
 
  • #16
The formula only tells you how much power is consumed in producing a given amount of thrust. It doesn't matter how fast the airplane is going. If the airplane is not moving, for example, the engine still puts out power and still produces thrust.
 
  • #17
David Lewis said:
The formula only tells you how much power is consumed in producing a given amount of thrust. It doesn't matter how fast the airplane is going. If the airplane is not moving, for example, the engine still puts out power and still produces thrust.

It does matter how fast the airplane is going though - the same amount of power will produce different amounts of thrust both based on the speed of the air traveling through the engine and the massflow of the air traveling through the engine. You really can't separate the two.
 
  • #18
GeForce7 said:
V_stall=39.18 m∕s or 141.10 km/h
  1. Landing must take place at 1.3 times the stall speed, but less than 180 km/h​
Those two don't work together.
 
  • #19
Hi guys, I would like to ask a question with regards to TSFC (Thrust Specific Fuel Consumption). The formula for calculating TSFC is fuel flow (kg/hour) divided by the thrust being generated by the engine at that point of time. Is it correct to assume that the fuel flow changes as you increase or decrease the thrust? If not, is the fuel flow constant? For example, the engine will burn less fuel (lower fuel flow) during cruising and burn more fuel (high fuel flow) during take-off?
 
  • #20
GeForce7 said:
Is it correct to assume that the fuel flow changes as you increase or decrease the thrust?
Sure.
 
  • #21
Airklners use movable extensions to change the airfoil shape
ever watch out the window on approach to landing? The wing becomes much wider and curved.
 
  • #22
jim hardy said:
Airklners use movable extensions to change the airfoil shape
ever watch out the window on approach to landing? The wing becomes much wider and curved.

They're called flaps and slats, specifically, and they're important in allowing the airplane to have an airfoil shape that can provide low drag in cruise while still being able to generate enough lift to land at a fairly low speed.
 
  • #23
Using an example taken from Wikipedia (https://en.wikipedia.org/wiki/Williams_FJ44#Specification), I took the values from FJ-44-1A and did some calculation.

Formula (https://www.grc.nasa.gov/www/k-12/airplane/sfc.html):

TSFC = Fuel Consumption in lb per hour/Thrust in lbf
0.456= Fuel Consumption in lb per hour/1900 lbf
Fuel Consumption in lb per hours=0.456*1900
Fuel Consumption in lb per hours=866.4 lb/h OR (392.99 kg/h)

Assuming my calculation is correct, the TSFC given by the manufacturer is for maximum thrust? If so, the fuel consumption at maximum thrust is 866 lb per hour (392.99 kg per hours)? Is there a way for me to calculate the fuel consumption at a certain thrust value (for example, during low speed cruise)?
 
  • #24
The power (as a function of thrust) formula I gave you gives you induced power, if my understanding is correct. Therefore power must be divided by the efficiency of the propulsion system.

System efficiency is sometimes divided into two parts: How efficiently chemical energy in the fuel is converted to heat and mechanical energy, and then what portion of that energy is converted to thrust.
 
  • #25
GeForce7 said:
Using an example taken from Wikipedia (https://en.wikipedia.org/wiki/Williams_FJ44#Specification), I took the values from FJ-44-1A and did some calculation.

Formula (https://www.grc.nasa.gov/www/k-12/airplane/sfc.html):

TSFC = Fuel Consumption in lb per hour/Thrust in lbf
0.456= Fuel Consumption in lb per hour/1900 lbf
Fuel Consumption in lb per hours=0.456*1900
Fuel Consumption in lb per hours=866.4 lb/h OR (392.99 kg/h)

Assuming my calculation is correct, the TSFC given by the manufacturer is for maximum thrust? If so, the fuel consumption at maximum thrust is 866 lb per hour (392.99 kg per hours)? Is there a way for me to calculate the fuel consumption at a certain thrust value (for example, during low speed cruise)?

Yes, TSFC is usually specified at full (non-afterburning) thrust. Unfortunately, there isn't an easy relationship to calculate fuel consumption at lower speeds - there are some calculations that can be done, but they usually end up rather complex (I'll dig out my propulsion textbook in a bit and see what it says).
 
  • #26
David Lewis said:
The power (as a function of thrust) formula I gave you gives you induced power, if my understanding is correct. Therefore power must be divided by the efficiency of the propulsion system.

System efficiency is sometimes divided into two parts: How efficiently chemical energy in the fuel is converted to heat and mechanical energy, and then what portion of that energy is converted to thrust.

I still don't believe your power formula is correct for any kind of power, but maybe I'm misunderstanding what you mean here by "induced power". Could you explain how you arrived at your formula?
 
  • #27
My hypothesis is that if you specify the diameter of the propeller, fan, or nozzle of your engine (called the actuator disk), then you know how much air (or gas) the system is able to work on. And as soon as you know the mass of that air then you know how much that mass must be accelerated in order to generate any specified thrust.

This gives you the induced power, which is the smallest possible amount of power required to generate a given amount of thrust. To that you need to also add in some power lost to friction in the bearings, gearbox, boundary layer, and unequal pressure distribution across the actuator disk.
 
  • #28
Yes, but without knowing the inflow velocity, you can't calculate any meaningful power number (you don't know how much acceleration you need to apply to the air, and you don't know the mass flow through your control volume), and your formula is missing the inflow velocity. Also, the smallest possible power to generate a given amount of thrust is zero, if you're allowed to fiddle with the parameters however you want.
 
  • #29
David Lewis said:
I believe the relationship between thrust and power is:
power = sq rt [(thrust cubed) divided by (2 * air density * area of actuator disk)]

What are the units of this power? Please show a dimensional analysis of your equation.
 
  • #30
That's an excellent point - I didn't even bother to check the units on that equation...
 
  • #31
My basic assumption is that, even if the propulsion unit is 100% efficient, it will still consume some power -- an unavoidable consequence of adding momentum to a fluid.
 
  • #32
But that power can be arbitrarily low by increasing the mass flow sufficiently. The power required for a given thrust depends on the energy required for a given change in momentum, which will depend both on inflow velocity and on the mass flow rate affected by the propulsion unit.
 
  • #33
David Lewis said:
The power (as a function of thrust) formula I gave you gives you induced power...
Perhaps you could provide an example. For instance, the 1903 Wright flyer produced 90 lbf thrust with two 8.5 ft long propellers.
 
  • #34
cjl wrote: "Yes, but without knowing the inflow velocity, you can't calculate any meaningful power number."

David Lewis wrote: Good catch. I forgot that kinetic energy is proportional to the square of velocity. It takes 3 times as much energy to increase the velocity of an air mass from 1.0 to 2.0 as it does from zero to 1.0. Yet delta v in both cases is the same. The power formula only applies to static thrust, if my reasoning is correct.

Acceleration seems to be greatest at the beginning, before rolling friction and air resistance come significantly into play, and initial acceleration is roughly equal to static thrust divided by gross takeoff mass. Acceleration gradually drops off to practically nothing before the airplane leaves the runway.
 
Last edited:
  • #35
David Lewis said:
Acceleration gradually drops off to practically nothing before the airplane leaves the runway.

I wouldn't necessarily say that's accurate - at 150mph or so, modern jetliners still have a rather dramatic excess of thrust, and can still accelerate fairly hard. Once they leave the ground though, they will tend to throttle back a bit, and once they reach climb speed, they also climb at a gradient such that the airspeed remains constant (so all the excess thrust goes towards climbing, rather than increased speed).
 
<h2>1. What is the definition of acceleration when it comes to an aircraft?</h2><p>Acceleration is the rate of change of an aircraft's velocity over a period of time. It is a measure of how quickly the aircraft is speeding up or slowing down.</p><h2>2. How is the acceleration of an aircraft measured?</h2><p>The acceleration of an aircraft can be measured using instruments such as an accelerometer or a rate gyro. These instruments measure the aircraft's change in velocity and calculate the acceleration based on that change.</p><h2>3. What factors affect the acceleration of an aircraft?</h2><p>The acceleration of an aircraft can be affected by various factors such as the thrust of the engines, the weight of the aircraft, the air resistance or drag, and any external forces acting on the aircraft.</p><h2>4. How is the acceleration of an aircraft calculated?</h2><p>The acceleration of an aircraft can be calculated using the formula: acceleration = change in velocity / time. This formula takes into account the initial and final velocities of the aircraft over a specific time period.</p><h2>5. Why is it important to determine the acceleration of an aircraft?</h2><p>Knowing the acceleration of an aircraft is important for several reasons. It helps pilots and engineers understand the performance and capabilities of the aircraft, and can also aid in the design and testing of new aircraft. Additionally, monitoring the acceleration can help detect any potential issues or malfunctions with the aircraft's systems.</p>

1. What is the definition of acceleration when it comes to an aircraft?

Acceleration is the rate of change of an aircraft's velocity over a period of time. It is a measure of how quickly the aircraft is speeding up or slowing down.

2. How is the acceleration of an aircraft measured?

The acceleration of an aircraft can be measured using instruments such as an accelerometer or a rate gyro. These instruments measure the aircraft's change in velocity and calculate the acceleration based on that change.

3. What factors affect the acceleration of an aircraft?

The acceleration of an aircraft can be affected by various factors such as the thrust of the engines, the weight of the aircraft, the air resistance or drag, and any external forces acting on the aircraft.

4. How is the acceleration of an aircraft calculated?

The acceleration of an aircraft can be calculated using the formula: acceleration = change in velocity / time. This formula takes into account the initial and final velocities of the aircraft over a specific time period.

5. Why is it important to determine the acceleration of an aircraft?

Knowing the acceleration of an aircraft is important for several reasons. It helps pilots and engineers understand the performance and capabilities of the aircraft, and can also aid in the design and testing of new aircraft. Additionally, monitoring the acceleration can help detect any potential issues or malfunctions with the aircraft's systems.

Similar threads

Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
4K
  • Introductory Physics Homework Help
Replies
6
Views
2K
Replies
4
Views
10K
  • Introductory Physics Homework Help
Replies
8
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Replies
63
Views
7K
  • Introductory Physics Homework Help
Replies
3
Views
763
  • Introductory Physics Homework Help
Replies
3
Views
2K
Replies
6
Views
1K
Back
Top