Understanding Different Forces acting on Vehicle

OBJECTIVE

The objective of this project is to get understand about different forces acting on a vehicle, i.e.

• Rolling Resistance Force
• Aerodynamic Drag Force
• Hill Climbing Force
• Acceleration Force

Evaluation and variation of different forces based on vehicle parameters using simple excel calculator.

Further based on overall tractive force, evaluation of vehicle performance characteristics using simple excel calculator.

About: Tire Code

Automobile tires are described by an alphanumeric tire code also called as ISO Metric tire code, mandated by U.S. Department of Transportation (DOT) but used worldwide.

P215/65R15 95H

• First initial optional letter (or letters) indicates vehicle class of tire
  • P: Passenger Car
  • LT: Light Truck
  • ST: Special Trailer
  • T: Temporary
• 3-digit number: Nominal section width of tire in millimetres
• 2- or 3-digit number: Aspect ratio of sidewall height as a percentage of nominal section width of the tire
• Second optional letter indicates construction of fabric of the tire
  • B: Bias belt
  • D: Diagonal
  • R: Radial
• 1- or 2-digit number: Rim diameter in inches of wheel
• 2- or 3-digit number: Load index indicates maximum weight limit per tire
• 1- or 22-digit/letter combo: Speed rating indicates maximum speed for the tire at full load

Below figure will help to decode load index and speed rating

Tire Code Decoding Illustrations:

	195 / 55 R 16 87V	90 / 100 R 10 53J	90 / 90 R 18 51P
Nominal section width	195 mm	90 mm	90 mm
Aspect ratio of sidewall height as a percentage of nominal section width of the tire	55%	100%	90%
Rim diameter	16 inches	10 inches	18 inches
406.4 mm	254 mm	457.2 mm
Maximum weight limit per tire	545 kg	206 kg	195 kg
Maximum speed for the tire at full load	240 kmph	100 kmph	150 kmph
66.67 mps	27.78 mps	41.67 mps

Excel Calculator: Maximum speed of motor @ specific speed

Calculation of maximum speed of motor used in electric scooter capable to run at 90 kmph, if fixed gear ratio is 7 for all the tire codes illustrated above using excel calculator.

Excel Calculator: Vehicle Propulsion Power

Vehicle propulsion power is evaluated based on tractive forces which are mentioned below:

• Rolling Resistance Force
• Aerodynamic Force
• Hill Climbing Force
• Acceleration

Simple illustration of an electric scooter has been considered below to evaluate vehicle propulsion. For ease, hill climbing force and acceleration force are ignored or can be said that problem is considered such that these two forces can be ignored. Here, climbing force is ignored as track considered is of zero inclination or zero gradeability. Also, acceleration force is ignored due to calculation being done at specific speed, i.e. maximum speed which can be achieved through tire at full based on the speed rating present in tire code.

Other than these forces, all forces are evaluated while considering the extreme values such as maximum weight (based on load index of tire), and maximum velocity (based on speed rating of tire). Also, rolling resistance is evaluated based on formula specified below which is typically acceptable for speeds upto 128 kmph.

`μ_(rr)=0.001(1+0.001v)`

The above shown vehicle propulsion power has been evaluated for extreme conditions irrespective of hilling climbing and acceleration force. Power is calculated at specific maximum speed which could be further extended to more realistic simulation using some standard drive cycles.

Effect of Tire Pressure Reduction by 15%

Suppose tire pressure reduction by 15% results in increase of rolling resistance, i.e. it’s effected by two times. While other parameters remain same such as maximum load, maximum speed, drag coefficient, etc. Then, we tried to observe the variation in total tractive force and total power output.

From the above results, what we can observe that due to 15% pressure drop in tire, the rolling resistance effect got doubled but since the aerodynamic force is dominating over the rolling resistance, much change can’t be seen in the total power irrespective of rolling resistance force being doubled.

Range Rover Sport Dragon Challenge

In year 2018, Land Rover successfully accomplished dragon road challenge using their first SUV class PHEV, i.e. Range Rover Sport edition. The challenge for PHEV was to generate required propulsion, gripping and balance in order to drive along dizzying 99 turns which is stretched to 11.3 km Tianmen Mountain Road (also called as Dragon Road) and to climb 999 steep steps to reach the Heavens Gate. These 999 steps were architected with gradeability of 100%, i.e. inclined at an angle of 45 degrees.It took almost 22 minutes 41 seconds to complete dragon challenge from the bottom of Tianmen Mountain Road.

Gradeability of 999 steep steps ≈ 100% (45 degrees)

Average speed of Range Rover Sport PHEV for total span of 99 turns and 999 steep steps ≈ 29.89 kmph

Definitely during the cornering pin turns, speed would be low below average speed. Also, during climbing steep steps and straight drag along the road, speed would be quite greater than the average speed that might be top speed or maximum power.

All four types of forces are acting on car, i.e. rolling resistance, aerodynamic drag, hill climbing and acceleration force. At the bottom of steps, acceleration force would dominate. Further during climbing the steps, hill climbing forces would dominate. As vehicle reaches the Heavens Gate, deacceleration force would dominate.