What should be the maximum height of center of gravity of the kart so that the kart slides sideways
instead of overturning.
Kart specifications:
Vehicle Mass = 60 kg
Rider Mass = 70 kg
Cd*A = 0.25 m2 (the Cd*A value is with the rider sitting on the seat)
Rolling resistance of tires = 0.01
Wheelbase = 1200 mm
Track Width = 1000 mm
Coefficient of friction between the road and the tire = 1.2
The test revealed that the kart was capable of accelerating at 9 m/s2 at start. The maximum power output
at the wheels is 7kW

To determine the maximum height of the center of gravity (CG) of the kart that allows it to slide sideways instead of overturning, we need to analyze the forces acting on the kart during a turn. The key factors include the vehicle's mass, the dimensions of the kart, and the friction between the tires and the road. Let's break this down step by step.

Understanding the Forces at Play

When a kart turns, two primary forces come into play: the gravitational force acting downwards and the lateral force due to acceleration or cornering. The kart will start to overturn if the moment created by the lateral force exceeds the stabilizing moment created by the weight of the kart acting through its center of gravity.

Key Parameters

• Vehicle Mass (m): 60 kg
• Rider Mass (M): 70 kg
• Total Mass (W): m + M = 130 kg
• Wheelbase (L): 1200 mm = 1.2 m
• Track Width (T): 1000 mm = 1.0 m
• Coefficient of Friction (μ): 1.2

Calculating the Maximum Height of the Center of Gravity

To find the maximum height of the center of gravity (h), we can use the following relationship:

1. Determine the Lateral Force

The maximum lateral force (F) that can be exerted without sliding is given by:

F = μ * W * g

Where g is the acceleration due to gravity (approximately 9.81 m/s²). Thus:

F = 1.2 * 130 kg * 9.81 m/s² = 1,588.56 N

2. Calculate the Moment about the Outside Wheel

When the kart is turning, the moment about the outside wheel due to the lateral force is:

Moment = F * (T/2)

Substituting the values:

Moment = 1,588.56 N * (1.0 m / 2) = 794.28 Nm

3. Calculate the Stabilizing Moment

The stabilizing moment due to the weight of the kart is:

Stabilizing Moment = W * g * (h)

Substituting the total weight:

Stabilizing Moment = 130 kg * 9.81 m/s² * h = 1,275.3h Nm

4. Set the Moments Equal for Stability

For the kart to slide instead of overturning, the lateral moment must be less than or equal to the stabilizing moment:

794.28 Nm ≤ 1,275.3h Nm

Now, solving for h:

h ≥ 794.28 Nm / 1,275.3 Nm = 0.623 m

Final Consideration

Thus, the maximum height of the center of gravity for the kart to slide sideways instead of overturning should be approximately 0.623 meters. Keeping the center of gravity below this height will help ensure stability during turns, allowing the kart to slide rather than tip over.

In practical terms, this means that when designing or modifying the kart, attention should be paid to the placement of the rider and any additional weight to maintain a low center of gravity. This will enhance performance and safety during high-speed maneuvers.