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Issue No 25, 1 May 2023
By: Anthony O. Ives
Issac Newton was an english physicist who discovered three principles that define equilibrium, forces and motion. Apparently Issac Newton was due to go to Cambridge university but could not go immediately due the great plague and instead stayed at home and came up with his three laws. Chances are if had went to university when he was suppose to he would not have discovered these three laws.
Newton's three laws are defined as follows:
A body remains at rest or travels in constant speed motion in constant direction unless acted on by a force.
The acceleration or deceleration force is directly proportional to rate of change of momentum with respect to time.
To every reaction there is an opposite and equal reaction.
An airplane or helicopter in steady level flight is a good example of the Newton's first law. In summary Newton's first law tells us in order to cause a change of direction or speed you will need to apply a force, in a airplane or helicopter this is generally through an increase or decrease in thrust as well as through forces produced by control surfaces or cyclic rotor pitch variation. The picture below shows an airplane in equilbrium or steady level flight.
Newton's second law is really related to the first law and is used to calculate the force needed to cause the change in speed or direction. Acceleration and deceleration is also experienced when direction is changing, in a later article circular motion will be discussed but something moving in circular motion is considered to be constantly accelerating as it is constantly changing direction. The most simple way to define Newton's second law is using an equation as below:
F = m a
Where F is force, m is the mass of the body and a is acceleration, force and acceleration are vector properties where as mass is a scalar property. Vector properties have direction in which the properties is acting along with the magnitude of the property. Scalar properties do not have direction just magnitude considering mass you can see how it would be impossible for it to have a direction.
The third law that Newton came up with states that if a force or moment is exerted on body then an opposite and equal force or moment must be produced. When you sit on a seat there an is opposite equal reaction to support your weight. However, Newton's third law is the explanation for why single rotor helicopters need a tail rotor, without a tail rotor a helicopter would continuously spin round. However, single rotor helicopters with tip jets on the rotor blades do not need a tailrotor as the force is being applied directly against rotor drag force and no moment is transferred through the rotor shaft.
The graphic below shows the forces and moment balance on a single rotor helicopter:
Moment or Torque is produced by applying a force at a certain distance on a lever which could produce a twisting motion. The equation for moment is given below:
M = F l
Where M is moment or torque, F is the force applied and l is the distance the force is applied from the centre point the moment or torque is produced about. A graphic illustration of moment is given below:
Further description of fundmental physics as applied to helicopters can be found in Ref [1].
Please leave a comment on my facebook page or via email and let me know if you found this blog article useful and if you would like to see more on this topic. Most of my blog articles are on:
Mathematics
Helicopters
VTOL UAVs (RC Helicopters)
Sailing and Sailboat Design
If there is one or more of these topics that you are specifically interested in please also let me know in your comments this will help me to write blog articles that are more helpful.
References:
[1] Principles of Helicopter Flight, 2nd Edition, W. J. Wagtendonk, 2006, Aviation Supplies & Academics
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