PPRuNe Forums - View Single Post - why is the ball in the middle ?
View Single Post
Old 30th Nov 2003, 01:55
  #5 (permalink)  
bookworm
 
Join Date: Aug 2000
Location: UK
Posts: 3,648
Likes: 0
Received 1 Like on 1 Post
i was under the impression that a turn was an un-equal force vector diagram ie NO SUCH THING AS CENTRIFUGAL FORCE
Centrifugal force is a fictitious force, an apparent force that needs to be there to account for the fact that you're trying to do physics in a spatial frame of reference in which Newton's Laws wouldn't otherwise work. Then again, so, according to Einstein, is gravity so let's not be too hard on it.

You can choose to look at the situation in one of two ways. You can either do the mechanics in an inertial reference frame fixed with respect to the earth, and look at the motion of the balance ball as it accelerates under the influence of gravity and the reaction at the turn and bank casing. Indeed those latter two forces are unequal so there is a net acceleration.

Alternatively, you can do the mechanics in a frame of reference fixed with respect to the aircraft that is rotating as it accelerates around the turn. If you do that you have to introduce a fictitious centrifugal force that acts on everything in the picture in proportion to its mass. The centrifugal force plus the gravity is opposed by the reaction at the turn and bank casing and there's no net acceleration in the frame of reference of the aircraft. Hence that's where the ball sits.

You can make your choice -- inertial frame, unbalanced forces and a net acceleration or accelerating frame, fictitious force, and (in this case) balanced forces and no net acceleration. For a case like this it doesn't make much difference, but for more complex situations it makes a lot of sense to simplify the model by using an accelerating frame and fictitious forces.

If you are prepared to combine gravity and centrifugal force (both of which are proportional to mass) into a single apparent gravity it offers another way of looking at the balance ball -- as an indicator of the direction of apparent gravity.
bookworm is offline