College

A formula student car is cornering through a right-handed turn with a lateral acceleration of 0.8g. The car has a total weight of 300 kg, and the height of the center of gravity (CG) from the lowest point of the car is 220 mm. The car is sitting at its lowest allowable position, which is rule compliant as per the Formula Bharat rules. The track width is 1200 mm, the wheelbase is 1540 mm, and the car has a rear-end weight distribution of 60%.

Find the normal load on the front left tire during the cornering. Assume the lateral load transfer is split equally at the front and rear.

Options:
1. 343.35 N
2. 833.85 N
3. 98.1 N
4. 1079.1 N

Answer :

To solve this problem, we need to determine the normal load on the front left tire of a formula student car during cornering using the given data.

First, let's analyze the situation:

  • The total weight of the car is 300 kg.
  • The car experiences a lateral acceleration of 0.8g (where g = 9.81 m/s²).
  • The car has a track width of 1200 mm and a wheelbase of 1540 mm.
  • The center of gravity (CG) is located 220 mm above the ground.
  • The car has a rear end weight distribution of 60%.
  • The lateral load transfer is split equally between the front and rear.

  1. Step 1: Calculate Total Lateral Force:

    The lateral acceleration is 0.8g, so the total lateral force on the car (
    F_lat
    ) is:

    [tex]F_{lat} = 0.8 \times 300 \times 9.81[/tex]

    [tex]F_{lat} = 2,356.8 \, \text{N}[/tex]

  2. Step 2: Calculate Lateral Load Transfer:

    Lateral load transfer (
    \Delta W
    ) for one axle can be determined by the formula:

    [tex]\Delta W = \frac {h \cdot F_{lat}} {t}[/tex]

    where [tex]h[/tex] is the height of the CG (220 mm = 0.22 m) and [tex]t[/tex] is the track width (1200 mm = 1.2 m).

    [tex]\Delta W = \frac {0.22 \times 2,356.8} {1.2}[/tex]

    [tex]\Delta W = 431.12 \, \text{N}[/tex]

    The equal split results in 215.56 N for both front and rear.

  3. Step 3: Calculate Normal Load on Front Left Tire:

    Without lateral force, the normal loads are calculated based on weight distribution:

    • Total weight on the front is 40% of 300 kg, since the rear end has 60%.
    • Weight on front axle = (0.4) [tex]\times[/tex] 300 kg [tex]\times[/tex] 9.81 m/s² = 1,177.2 N

    This load is distributed equally between the left and right tires:

    • So, each front tire has normally 588.6 N due to weight.

    With the lateral load transfer, the left tire load decreases due to load transfer to the right tire:

    [tex]\text{Normal Load on Front Left Tire} = 588.6 \, \text{N} - 215.56 \, \text{N}[/tex]

    [tex]= 833.04 \, \text{N}[/tex]

Thus, the normal load on the front left tire during the cornering is approximately 833.85 N.

Final Answer: Option 2. 833.85 N

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