Average Passenger Plane Terminal velocity with added speed

In summary: You could probably reach about 500 m/s in around 20 seconds, which is about 1100 mph.[/QUOTE] In summary, if a passenger plane with a mass of 72574.7792 kg and traveling at a speed of 500 knots lost control and went down at a 40 degree angle, it would take approximately 20 seconds to reach a speed of 500 m/s before hitting the ground, assuming a drag coefficient of 0.012 and a frontal area of 10 m^2. However, the terminal velocity of the plane would be around 2800 m/s, which may not be reached in the short amount of time before impact.
  • #1
A passenger plane is traveling at a speed of 500 knots, has a mass of 72574.7792 kg, and has an altitude of 35,000 feet. If the pilot lost control of the plane and couldn't reduce speed or anything and the plane was going down at approximately a 40 degree angle, how long would you have until it hit the ground?

This is just curiosity btw, so if it is too hard to find out, then don't worry about it
 
Physics news on Phys.org
  • #2
ThePizzaDeliveryGuy said:
A passenger plane is traveling at a speed of 500 knots, has a mass of 72574.7792 kg, and has an altitude of 35,000 feet. If the pilot lost control of the plane and couldn't reduce speed or anything and the plane was going down at approximately a 40 degree angle, how long would you have until it hit the ground?

This is just curiosity btw, so if it is too hard to find out, then don't worry about it
Welcome to the PF.

Have you had trigonometry yet in school? That's the easiest way to figure out this problem.
 
  • #3
berkeman said:
Welcome to the PF.

Have you had trigonometry yet in school? That's the easiest way to figure out this problem.
No i have not had it yet
 
  • #4
berkeman said:
Welcome to the PF.

Have you had trigonometry yet in school? That's the easiest way to figure out this problem.

Only if you neglect air resistance. Given that the title included the phrase "terminal velocity", that would imply that the question is not intended to neglect air resistance. In that case, this is not a simple problem to solve. You'd have to simply estimate to some arbitrary (and likely poor) level of accuracy.
 
  • #5
That is a pretty steep decent so I assume the plane's speed would go higher than a normal cruise speed or any safe speed. The terminal speed is not something that would normally be studied or published, so you will have to make some assumptions. And of course, the terminal speed is the main thing that would determine the time before the crash.
 
  • #6
ThePizzaDeliveryGuy said:
has a mass of 72574.7792 kg
That is quoting the mass to the precision of 1/10 of a gram. You would have been better off to say 160,000 pounds.
 
  • #7
boneh3ad said:
In that case, this is not a simple problem to solve.
True, but I assumed that the speed would not be much more than 500 knots. Maybe that was too much of a simplification on my part.
 
  • #8
ThePizzaDeliveryGuy said:
This is just curiosity btw, so if it is too hard to find out, then don't worry about it

Then download X-Plane and try it out. Much more fun than trying to calculate something like this.
http://www.x-plane.com/desktop/home/
 
  • #9
berkeman said:
True, but I assumed that the speed would not be much more than 500 knots. Maybe that was too much of a simplification on my part.

Regardless of speed, air resistance complicated matters substantially. If there was no resistance then it is sime kinematic a. If it was a sphere with air resistance, that's relatively easy to estimate. But with a plane, it will depend so much on what orientation the plane has as it is falling that it's an intractable problem.
 
  • #10
ThePizzaDeliveryGuy said:
A passenger plane is traveling at a speed of 500 knots, has a mass of 72574.7792 kg

Looks like an insect sneaked on board that day and pushed the weight up an extra 0.2g. :-)
 
  • Like
Likes FactChecker
  • #11
Clearly, we need to make some gross approximations.
Here is a table of some typical drag coefficients. http://www.engineeringtoolbox.com/drag-coefficient-d_627.html
If we take the plane to have a drag coefficient of ##c_d = 0.012##, and a frontal area of ##A = 10 m^2##, and density of air ##\rho = 1.2 kg/m^3##,
##F_d = c_d \rho v^2 A##
Terminal velocity ##v_f## is reached when the vertical component of the drag equals the force of gravity.
##mg = F_d \sin 40^o##
therefore
##v_f = \sqrt{ \frac{mg}{c_d \rho A \sin 40^o}}##
~ 2800 m/s
Is it really that high? Maybe the drag is higher than 0.012.

Anyways, you probably wouldn't have enough time to reach terminal velocity.
 
  • Like
Likes FactChecker

1. What is terminal velocity and how is it affected by added speed?

Terminal velocity is the maximum speed that an object can reach when falling through the air. It is dependent on the object's mass, surface area, and the density of the air. When an object is falling, it will continue to accelerate until it reaches a point where the force of air resistance is equal to the force of gravity, causing it to reach a constant speed. Adding speed to an object will not affect its terminal velocity, as it will still reach the same maximum speed due to the balance of forces.

2. What is the average terminal velocity of a passenger plane?

The average terminal velocity of a passenger plane is approximately 150-180 miles per hour. This can vary depending on the type of plane, its weight, and the weather conditions.

3. How does air density affect the terminal velocity of a passenger plane?

Air density plays a significant role in determining the terminal velocity of a passenger plane. In denser air, there is more resistance, causing the object to reach its terminal velocity at a lower speed. In less dense air, there is less resistance, and the object will reach its terminal velocity at a higher speed.

4. What factors can increase the terminal velocity of a passenger plane?

The two main factors that can increase the terminal velocity of a passenger plane are weight and surface area. A heavier plane will fall faster than a lighter one, and a larger surface area will experience more air resistance, causing it to reach its terminal velocity at a lower speed.

5. Is the terminal velocity of a passenger plane the same during takeoff and landing?

No, the terminal velocity of a passenger plane is not the same during takeoff and landing. During takeoff, the plane is accelerating and has not yet reached its maximum speed. During landing, the plane is decelerating and will not reach its terminal velocity as it is being controlled by the pilot. The plane's terminal velocity is only reached when it is in freefall, such as during a steep descent or in an emergency situation.

Suggested for: Average Passenger Plane Terminal velocity with added speed

Replies
1
Views
698
Replies
10
Views
1K
Replies
6
Views
945
Replies
12
Views
536
Replies
19
Views
16K
Back
Top