Forces Acting on a Vehicle

• 195 – Width. This number is the maximum width of the tyre. It is measured in millimetres from sidewall to sidewall. This width is standardised by the manufacturer depending on the vehicle. It plays an important role in vehicle handling, traction and fuel consumption and hence needs to be taken care of when choosing new tyres.
• 55 – Aspect Ratio. This number following the slash is called Aspect Ratio. This is the ratio of the height of the tyre's cross-section to its width. For example – 55 means that the height is equal to 55 per cent of the tyre's width. If the aspect ratio is higher, the sidewall of a tyre will be taller. Heavy vehicles have tyres with aspect ratios as high as 95 per cent. A higher aspect ratio may compromise on handling, but it provides a more comfortable ride. Meanwhile, high-performance cars have a low aspect ratio, thus providing a better handling and reduced rolling around the corners, while compromising on ride comfort.
• R – Construction. The alphabet following the aspect ratio indicates the tyre construction. The R, in this case, stands for Radial. B will indicate that the tyre is a bias ply type tyre. The construction of the tyre helps us understand the characteristic of the tyre.
• 16 – Wheel Diameter. The number here denotes the diameter of the wheel. It is the OD of the rim/alloy that will be wrapped around by the tyre. This dimension is the most important number here since the selection of the tyre depends on the size of the rim.
• 87 – Load Index. The load index relates to the maximum load-carrying capacity of the tyre. The lower profile tyres tend to have lower load ratings compared to higher profile ones. Fitting an incorrect load rating will seriously compromise on safety and can result in a serious accident. This number is just an index and need to be checked with the corresponding weight (in kgs) in the manufacturer’s tabloids.
• V – Speed Rating. Similar to load index, the speed rating is the maximum service speed your tyre is capable of maintaining. The speed rating will give you the speed you tyre can endure without failure. Speed ratings are specific for passenger car tyres and not light truck tyres. It is essential to keep in mind the corresponding speeds to the speed rating before pushing the car to its limits, to prevent unforeseen failures.

Maximum Speed of the Motor used in Electric Scooter:

i) Given:

Linear Velocity = 90 kmph = 25 m/s

Gear Ratio = 7

Tire Size = 90/100 R10 53J

Angular Velocity:

ω = G*v/r

where,

• G = Gear ratio
• v = linear velocity(m/s)
• r = radius of tyre

Radius of Tyre:

Tyre Height = Aspect ratio * width/100

= 100 * 90/100

Tyre Height = 90 mm

Tyre Diameter = 25.4*Wheel Diameter + 2*Tyre Height

= 25.4*10 + 2*90

Tyre Diameter =434 mm

Tyre Radius = 217 mm = 0.217m

Angular Velocity, ω = G*v/r

= 7 * 25/0.217

= 806.45 rad/s

Angular Velocity = 7705 RPM

ii) Given:

Linear Velocity = 90 kmph = 25 m/s

Gear Ratio = 7

Tire Size = 90/90 R18 51P

Radius of Tyre:

Tyre Height = Aspect ratio * width/100

= 90 * 90/100

Tyre Height = 81

Tyre Diameter = 25.4*Wheel Diameter + 2*Tyre Height

= 25.4*18 + 2*81

Tyre Diameter =619.2 mm

Tyre Radius = 309.6 mm = 0.3096 m

Angular Velocity, ω = G*v/r

= 7 * 25/0.3096

= 565.2 rad/s

Angular Velocity = 5400 RPM

2. Prepare a simple excel calculator to identify vehicle propulsion power based on given inputs and outputs.

Formulae Used:

Rolling Resistance Force:

Frr = μ*m*g

Air Drag Force:

Fad = 1/2*ρ*A*Cd*v^2 (N)

Total Power at given speed = (Rolling Resistance Force + Air Drag Force)*Speed

What are the limitations of this calculation?

• The coefficient of rolling resistance is constant but in depends on tyre pressure & road conditions.
• Air density also taken as constant but it varies with respect to temperature, pressure & other factors.
• Drag coefficient varies on aerodynamics of the car it also considered as constant.

3. Assuming that tire pressure reduction by 15% results in increase of rolling resistance effect by two times, how much will be the difference in total traction power keeping all other parameters same?

• As per the given statement when the tire pressure is reduced by 15% the rolling resistance effect increases by two times.
• When rolling resistance coefficient increase by two times the rolling resistance force is also increased by two times.
• And the total traction power is increased by 1.5 times.

4. Dragon Challenge:

How much is the gradeability? What was the average speed? Which are the forces acting on car?

• The gradeability of the vehicle is 45 degree or 100% will climbing the steps.
• The average speed of the vehicle during 99 turns hill is 80kmph and while climbing the steps the average speed is 35kmph
• The forces acting on a car during 99 turns & 999 steps are

i. Hill Climbing Force

ii. Rolling Resistance Force

iii. Aerodynamic Drag Force

iv. Centripetal Force

v. Acceleration Force

Attachment:

The link for vehicle power requirement calculation is given below:

https://docs.google.com/spreadsheets/d/10ChJ0bqeOgxPMgtazDi6xw7Fz-LlpqLw7yo1XF6lR4M/edit?usp=sharing