Radius of largest possible loop of an Airplane.

In summary, the problem asks for the radius of the largest circular loop possible for a 2250 kg airplane traveling at a speed of 320 km/hour and the force on the plane at the bottom of this loop. Using the conservation of energy and assuming no thrust, no drag, and a constant speed, the "critical speed" can be determined as the square root of the radius multiplied by the gravitational force. Plugging this into the equation for conservation of energy, the radius can be solved for. However, the assumptions made in the problem statement may not accurately reflect real-life conditions and may not lead to the maximum possible radius.
  • #1
HRubss
66
1

Homework Statement


A 2250 kg airplane makes a loop the loop (vertical circle) at a speed of 320 km/hour. Find (a) the radius of the largest circular loop possible and (b) The force on the plane at the bottom of this loop.

Homework Equations


F = m*a
Centripetal Force = m * (v2)/r
"Critical Speed" = Sqrt ( r*g) (I'm not sure if that's the proper term)
1/2 *m*v2 = 1/2*m*v2

The Attempt at a Solution


Since no height was given in the problem, I set the altitude of the plane at 0 so it shouldn't have any potential energy at the bottom of the loop. Using the conservation of energy and 0 potential energy, I have the 3rd equation. I also know that the "critical speed" is equal to the square root of the radius * gravitation force so I substitute that into my final kinetic energy's velocity and solve for the radius. I'm not sure if this is correct and I know that the normal force is dependent on the finding the correct radius, I don't attempt part b just yet.
 
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  • #2
The problem statement is a bit weird because (a) airplanes have thrust and (b) airplanes have wings. It is unclear what you are supposed to assume. No thrust and no drag (=conservation of energy is useful)? Constant speed? "Feet down" feeling at the top (=the critical speed applies)? Or nearly zero speed at the top?
Assuming no thrust, no drag, and "feet down" feeling: At which height does the airplane need this critical speed (or, asked differently: where is this the limiting factor)? You can plug that into an equation for the conservation of energy and solve for r.
 
  • #3
I agree question is a bit problematical.

I would assume that the pilot maintains a constant speed.
I probably wouldn't assume the pilot experiences positive g ("feet down" feeling) at the top because I think that implies a loop of bigger radius is possible.
 
  • #4
My guess is you are supposed to pretend that the airplane is not capable of flying upside down for an extended period, i.e. that it can generate no lift when inverted. So at the top of the loop it is behaving like a wingless rocket, or even a projectile.
 
  • #5
CWatters said:
I agree question is a bit problematical.

I would assume that the pilot maintains a constant speed.
I probably wouldn't assume the pilot experiences positive g ("feet down" feeling) at the top because I think that implies a loop of bigger radius is possible.
This combination of assumptions doesn't lead to a maximal radius.
 

FAQ: Radius of largest possible loop of an Airplane.

What is the radius of the largest possible loop an airplane can make?

The radius of the largest possible loop an airplane can make is dependent on several factors, including the type of airplane, its weight, and its speed. Generally, it is recommended for pilots to maintain a radius of at least 2,000 feet for safety purposes.

Why is the radius of the largest possible loop important for airplanes?

The radius of the largest possible loop is important for airplanes because it determines the amount of centrifugal force that the airplane will experience during the maneuver. Too small of a radius can put excessive stress on the airplane's structure, which can lead to structural damage or even failure.

Can all airplanes perform a loop with the same radius?

No, not all airplanes can perform a loop with the same radius. The ability to perform a loop depends on the airplane's design and capabilities. Generally, fighter jets and aerobatic airplanes have a smaller radius of loop compared to commercial airliners.

What are the potential risks associated with performing a loop with a large radius?

The potential risks associated with performing a loop with a large radius include exceeding the airplane's structural limits, loss of control, and disorientation of the pilot. It is important for pilots to carefully calculate and plan their maneuvers to ensure the safety of the flight.

How can pilots determine the radius of the largest possible loop for their airplane?

Pilots can determine the radius of the largest possible loop for their airplane by consulting the aircraft's performance charts and taking into consideration the weight, speed, and altitude of the airplane. They can also consult with experienced pilots or flight instructors for guidance and recommendations.

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