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Tech Talk | Weights and rotating masses in karts
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WEIGHTS AND ROTATING MASSES IN KARTS
13 October 2017
A kart consists of several elements of a certain weight. This results in so-called motion inertia, i.e. the force opposing acceleration. It is an important factor and deserves further analysis
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WHAT IS IT?
HOW DOES IT WORK?
IN PRACTICE
All objects that have a mass observe the laws of physics and, in particular, the equation of motion. The axiom, in itself, can be found on the first pages of any basic physics book, but its practical implications are not as easy to analyse, especially when, as in karting, they can become crucial to achieving top performance.
Let’s start with the theory: excluding all forms of friction that can exists in reality, the motion equations can be simplified according to the following formulas:
Rotating motion: T = I * w
where T is torque applied to the object, I is the moment of angular inertia and w is angular acceleration, i.e. the acceleration of the rotating masses (which in karts
are represented by tyres, wheel rims, brake disc, chain, plate, etc.).
Linear motion: F = m * a
where F is the linear thrust force, m the overall mass of the kart and a the linear acceleration.
Transforming the formulas into practice means that acceleration, both linear (a) and angular (w), are directly dependent on force (which generates the linear displacement of the objects) and torque (force that generates the rotation of objects). Whereas it is inversely proportional to the mass (m) and moment of inertia (I).
Basically: the more a vehicle weighs and has heavy rotating masses, the greater the torque and the force needed to accelerate.
WEIGHT IS THE FACTOR THAT DETERMES MOTION INERZIA, BOTH FOR LINEAR AND ROTATING MOTION
WHAT IS IT?
HOW DOES IT WORK?
IN PRACTICE
Focussing on the specific components of a kart, we can say that inertia is determined by simple masses (such as the driver’s weight, the weight of the engine and the chassis, with tank and fuel), which determine the parameter ” m “, and rotating masses (tyres, wheel rims, disc brake, chain, plate, etc.) that determine the instant inertia “I”. Regarding the masses “m”, the situation is simple, since they are determined by the overall weight of the kart (and engineered) plus the driver. The moment of inertia, on the other hand, does not depend solely on the weight of the rotating objects, but also by the square of the distance of the masses from the centre of rotation (radius r).
WHAT IS IT?
HOW DOES IT WORK?
IN PRACTICE
For example, let’s take a disc that rotates: its moment of inertia is given by the formula:
I = m * R2
R is the radius of the disc and m is the mass.
However, if we consider the brake disc, which is actually a plate, the moment of inertia formula becomes:
I = m * (Re2 – Ri2)
where Re is the outer radius and Ri the inner radius.
As a result, the greater the outer radius of the disc or plate, the greater the moment of inertia I, i.e. the resistance to acceleration.
Clearly, the greater the inner radius (i.e. the thinner the disc plate), the less it will be I.
Added to this is that the dependence of the moment of inertia on the radii, both inner and outer, is square and, therefore, their measurement will have a greater
effect compared to the total weight of the disc.
Let’s look at an example to gain a better understanding.
On the one hand, a cast iron disc weighing 1 kg, with a 9 cm outer radius and a 7 cm inner radius. Reasonable values for a traditional rear brake disc.
On the other hand, a disc with a mass weighing about half of the former, i.e. 0.6 kg, perhaps made of Ergal (aluminium alloy), with a 7 cm inner diameter (i.e. with a disc plate of the same width as the former), but with an 11 cm outer diameter. The respective moments of inertia will be:
Ighisa = 1 * (922 – 72) = 32 kg m2
Iergal = 0,6 * (112 – 72) = 43,2 kg m2
Despite the disc made of Ergal being almost half the weight, its moment of inertia is considerably higher than the brake disc made of cast iron due to an outer diameter that is only 2 cm greater.
THE HEAVIER THE KART AND THE MORE ROTATING MASSES IT HAS, THE GREATER THE INERTIA OPPOSED TO ACCELERATION AND, THEREFORE, THE GREATER THE POWER REQUIRED FROM THE ENGINE
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