Physics applied to wheelchairs

Basic Concepts:

CENTER OF GRAVITY (CG)

The Center of gravity is an imaginary point in a body of matter where, for convenience in certain calculations, the total weight of the body may be thought to be concentrated.

FREE BODY DIAGRAM (FBD)

A free body diagram is a graphical illustration with the intent to help us visualize the applied moments, forces and resulting reactions on a body in a certain condition.

MOMENT

A moment is the turning effect of a force that may cause an object to turn. It is calculated by multiplying the force times the perpendicular distance from the pivot point (which is the shortest distance between the pivot and the line of action of the force).

MASS

Mass is both a property of a physical bodymand and a measure of its resistance to acceleration when a net force is applied.

ACCELERATION

Acceleration is the rate of change to the velocity of an object within a certain time.

Physics applied to wheelchairs:

If the object is stationary, in the free body diagram, both the forces and moments need to add up to zero. This is important because if you have the weight of the person in the chair, the location of her CG and the distance between the wheels, you can calculate the forces on the wheels using moments.

As to balance, it is crucial to know that when the center of gravity of the user is vertically aligned with the point where the wheel contacts the ground, the chair will be extremely unstable, to the point where if the angle formed between the bottom of the wheelchair and the ground (which is the tipping angle) increases, the wheelchair will fall over. This happens because there is no moment to counteract the moment that the Center of Gravity generated, and a wheelchair tips over when the moments and the forces that are acting on it become unbalanced.

If we think about the wheels, there are many things that we can do to completely alter them. If the wheelchair has bigger wheels, that makes it easier for the wheelchair user to operate it by themselves. This is related to the torque, which can be described by the need to exert a Force (F) on the object at a distance (r) from the center of rotation. It causes a change in the rotational motion of the wheel. In this circumstance, you can calculate the torque with this formula:

Torque= force (F) x distance (r)

Therefore, the bigger the radius of the wheels, the easier it is to make them spin, since the torque is related to the acceleration of the wheelchair (the bigger the torque, the bigger the acceleration). That being said, with bigger wheels, it takes the person less effort to move around compared to what it would take if the wheel was smaller because the force for the torque will be made by the user’s arm .

Usually, to simplify the physics, we use the center of gravity, also referred to as the center of mass, even though the weight of the wheelchair is distributed over the front and rear wheels.

If we move the Centre of Gravity backwards and upwards, the weight on the rear wheels will be increased, making the chair easier to handle, but also more unstable. On the other hand, if we move it down and forward, the chair gains stability but is more difficult to handle. The best thing to do is to try to conjugate these two ideas in order to have the perfect balance between having a chair that is easy to handle and stable. With that being said, since the weight usually rests more on the rear wheels, the closer the center of gravity is to the rear axle, the better. There are various reasons as to why this is prefered. For starters, it will decrease the rolling resistance, which is the force resisting the motion when a body rolls on a surface.

Given that the formula to calculate the rolling resistance coefficient is:

F=CrrN

where:

F stands for rolling resistance force (R)

Crr is the dimensionless rolling resistance coefficient or coefficient of rolling friction (it is the force needed to push a wheeled vehicle forward, at a constant speed, on a level surface, or zero grade, with zero air resistance, per unit force of weight)

N is the normal force, the force perpendicular to the surface on which the wheel is rolling.

If we take Newton’s third law (the Law of Reaction) that states that for every action (force) there is an equal and opposite reaction, we can state that the more weight there is pushing the wheel down to the floor, the more the floor pushes back. Therefore, the more weight there is on the wheel, the bigger the normal force will be, which will increase the rolling resistance. Since the rolling resistance decreases with the wheel diameter, the rear wheels provide less resistance, making it more advantageable to put on more weight on the rear wheels. Of course, that means there will be an increase in the rolling resistance of the big rear wheels, but it's not as large as the decrease on the front wheels.

The basketball wheelchairs, as well as many other wheelchairs like padel or tenis ones, have their wheels inclined inwards at the top. This reduces the rolling resistance, and increases the lateral stability of the chair, but also increases the width, which may restrict access.

The rolling resistance can also be altered by the material that the tyres are made from, the material the floor is made of or the air pressure in the tyres (in case the person uses pneumatic tyres).

Newton’s second law explains how much motion is created by a force. It affirms that:

Force = mass x acceleration

Using this formula, we can understand that the acceleration an object experiences is proportional to the size of the force (the bigger the acceleration, the bigger the force) and inversely proportional to the object’s mass (because acceleration=forcex 1:mass, meaning that the bigger the mass is, the smaller the acceleration will be).

This being said, the less the wheelchair weighs the better, because the lighter the mass of the wheelchair jointly with the mass of the user is, the less effort needs to be put into moving the wheelchair.

There are a few problems with making a wheelchair lighter, because not only does it usually involve using expensive materials but we also need to take into consideration the stiffness of the materials. Since any bending in the wheelchair structure will waste effort that should’ve been transmitted into forward motion, the materials used need to resist bending whilst in motion.