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# The Physics of Inertial Training

For an optimal understanding of how inertial machines work, the first important step to take is to have a clear knowledge of the basic physics principles behind the concept of inertial training.

This is fundamental since not having a basic knowledge in physics will lead us to erroneous conclusions as well as doing wrong comparisons between different types of equipments.

Inertial (or flywheel) machines work under the principle of the accelerated Uniform Circular Motion, which is completely different principle from the one of Linear Motion associated with the traditional movement of free weights.

The circular movement starts from a formula that is as follows:

Moment = Moment of inertia x angular acceleration

If we start to break these formulas down for a deep analysis we can see that mathematics of circular motion gives great importance to the radius, which is always raised to the square in its formulas, while the mass is being multiplied by a reducing coefficient (1/2 and 3/10).

The reason is simple because as soon as the mass rotates around an axis, the gravity of the mass has little or no importance while the radius is fundamental.

Graphic representation showing a flywheel with its radius

Going deeper into physics, we can see that as soon as the flywheel starts to rotate on itself and we want to calculate the work being done, mathematics tells us that the formula is:

1/2 Moment of inertia x rotation speed squared

(because in this case we start at a 0 speed value).

Once again, mathematics tells us that speed is much more decisive than inertia for calculations, and specifically it is the final speed being reached that is important: what is fundamental is the acceleration capacity of the machine.

The metric on which we are going to work is power, which is defined by the formula: work/time.

In very simple terms, by developing a flywheel machine that accelerates as much as possible, it will happen that during a defined exercise with a fixed distance (range of motion), whenever the speed of rotation of the flywheel is increased, two very interesting things happen: the first one is that speed will increase to the square for the mathematics, and as a consequence of this higher speed, the time it will take to complete the movement will be significantly reduced.

This is the simple reason why the ability for the flywheel machine to accelerate is the key, and for this we must fight against the biggest enemy of circular motion, namely the loss of energy due to friction and elasticity of the rope.

The concept behind these machines is the same as that of a racing bike, where all the force exerted by the cyclist on the pedal (in our case on the grip) is transmitted quickly and directly from all the elements of the bike (in our case pulleys-rope) to move as far as possible. The difference in costs and prices lies in the materials being used, which make the difference in terms of energy loss and efficiency of the athlete's effort. Poor quality inertial machines will make it difficult, because of their energy losses, to detect small improvements or worsening, which is harmful especially in elite performance where the details make the difference.

Ramon is a performance expert from Vigo (Spain); he has studied Sport Sciences at Vigo University and he has obtained a Master in High Performance at the Universidad Autonoma de Madrid and a Master in Biomechanics at the Biomechanics Institute of Valencia.

Ramon has experience in using flywheel machines since 2007 and actually he is the owner and founder of the spanish company Einercial.