Force acting on Vehicle
AIM:-
To Calculate the maximum speed of a vehicle and propulsion power.
PLATFORM USED:-
Software – Microsoft Office Excel.
SYSTEM SPECIFICATIONS:-
- Manufacturer – Acer
- Model – ASPIRE E1-531
- Operating System – windows 7 Ultimate
- Processor – Intel(R) Pentium(R) CPU B960 @ 2.20GHz 20GHz
- RAM – 4 GB
OBJECTIVE:-
- To calculate the maximum speed of the motor used in electric scooter capable to run at 90 kmph.
- Prepare the Simple Excel calculator to evaluate vehicle propulsion power based on given inputs and outputs.
- To find the difference in total power.
- To determine the Gradeability the average speed of Range rover sport dragon as per provided inputs.
GOVERNING EQUATION:-
- Diameter of the tire,
`D_t=(2. H_s)+D_r`
Where,
`D_t=Diameter of Tire (m)`
`W_s=Section Width (m)`
`AR=Aspect ratio`
`H_s=Section height (AR % of W_s)`
`D_r=Diameter of rim (m)`
- Angular Velocity,
`ω= v/r .G`
where,
`ω=Angular velocity (rad/sec)`
`v=velocity (m/s)`
`r=Radius (m)`
`G=Gear Ratio`
- Rolling Resistance Force,
`F_rr= μ_rr .m .g`
Where,
`F_rr=Rolling Resistance Force (N)`
`μ_rr=Rolling Resistance co-efficient`
`m=Mass(kg)`
`g=Gravity (m/s^2 )`
- Aerodynamic Drag Force,
`F_ad=0.5 .ρ .A .C_d .v^2`
Where,
`F_ad=Aerodynamic Drag Force (N)`
`ρ=Air Density (kg/m^3 )`
`A=Area (m^2 )`
`C_d=Co-efficient of drag`
`v=Velocity (m/s)`
- Tractive Effort Force,
`F_te= F_rr+ F_ad`
where,
`F_te=Traction Effort force (N)`
`F_rr=Rolling Resistance Force (N)`
`F_ad=Aerodynamic Drag force (N)`
SOLUTIONS:-
- To calculate the maximum speed of the motor used in electric scooter capable to run at 90 kmph.
THEORY:-
Tire nomenclature:
Load Index:
Load Index is the numerical value representing the maximum weight, a tire can carry. For the selected tyre, Load Index is 53, which corresponds to a load capacity of 206 Kg.
Mast passenger vehicle have a Load Index Value ranging from 20 to 120.
Speed Symbol:
Speed Rating, represented by an alphabet that denotes the maximum “Vehicle Speed” a certain Tyre can withstand.
While carrying a load corresponding to its Load Index. Speed Rating of Selected tyre is “J” which refer to maximum speed capacity of 100 km/h.
Given Data:-
- Tire Code 1 - 90/100 R10 53J
- Tire Code 2 - 90/90 R18 51P
- Velocity - 90 Kmph = 25 m/s
- Gear Ratio - 7
To Find :-
1. `v_max of tire 1= ?`
2. `v_max of tire 2= ?`
CALCULATION :-
TIRE -1
Extracting the data from the tire 1 specification,
90/100 R10 53J
Section width (`W_s`) = 90 mm = 0.09 m
Aspect Ratio (AR)= 100%
Section Height (`H_s`) = 90 * 100% = 0.09 m
`H_s=Section height (AR % of W_s)`
Rim Diameter (`D_r`) = 10 inch = 0.254
Calculating the tire diameter,
`D_t=(2. H_s)+D_r`
`D_t=(2*0.09)+ 0.254`
`D_t=0.18+0.254`
`D_t=0.434 m`
Calculating the Tire Radius,
`R_t= D_t/2`
`R_t= 0.217 m`
Calculating the Angular velocity,
`ω= v/r .G`
`ω= 25/0.217 .7`
`ω=806.45 rad/sec`
Calculating the Maximum Speed,
`v_max of T1= ω .r`
`v_max of T1=806.45*0.217`
`v_max of T1=174.99 m/s`
`v_max of T1=630 kmph`
TIRE -2
Extracting the data from the tire 2 specification,
90/90 R18 51J
Section width (`W_s`) = 90 mm = 0.09 m
Aspect Ratio (AR)= 90%
Section Height (`H_s`) = 90 * 90% = 0.081 m
`H_s=Section height (AR % of W_s)`
Rim Diameter (`D_r`) = 18 inch = 0.4572 m
Calculating the tire diameter,
`D_t=(2. H_s)+D_r`
`D_t=(2*0.081)+ 0.4572`
`D_t=0.162+0.4572`
`D_t=0.6192 m`
Calculating the Tire Radius,
`R_t= D_t/2`
`R_t= 0.310 m`
Calculating the Angular velocity,
`ω= v/r .G`
`ω= 25/0.310 .7`
`ω=564.51 rad/sec`
Calculating the Maximum Speed,
`v_max of T2= ω .r`
`v_max of T2=564.51*0.310`
`v_max of T2=174.99 m/s`
`v_max of T2=630 kmph`
Results:-
`v_max of T1=630 kmph`
`v_max of T2=630 kmph`
- Prepare a simple Excel calculator to indentify Vehicle Propulsion Power based on Given Inputs and Outputs
ROLLING RESISTANCE FORCE:
Rolling Resistance, sometime called rolling friction or rolling drag, is the force resisting the Motion when body (such as a Ball, Tyre or wheel) roll on a surface. It is mainly caused by Non-Elastic effect; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc.
A Formula for Rolling Resistance force is given below:
`F_rr= μ_rr .m .g`
Where,
`F_ad=Aerodynamic Drag Force (N)`
`ρ=Air Density (kg/m^3 )`
`A=Area (m^2 )`
`C_d=Co-efficient of drag`
`v=Velocity (m/s)`
AERODYNAMIC DRAG FORCE:
The force on an object that resists its motion through a fluid is called “Drag”. When the Fluid is a gas like “Air” it is called Aerodynamic drag or Air Resistance.
`F_ad=0.5 .ρ .A .C_d .v^2`
Where,
`F_ad=Aerodynamic Drag Force (N)`
`ρ=Air Density (kg/m^3 )`
`A=Area (m^2 )`
`C_d=Co-efficient of drag`
`v=Velocity (m/s)`
The Drag co-efficient is a function of several parameters like shape of the body, Reynolds number for the flow, Mach number and Roughness of the Surface.
TOTAL TRACTIVE FORCE:
The term tractive efforts are often used synonymously with tractive force to describe the pulling and pushing capability of a locomotive. In an Automotive Engineering, the terms are distinctive; tractive efforts are generally Higher than tractive force by the amount of Rolling Resistance present.
`F_te= (T*G)/R`
Where,
T = Motor torque.
G = Gear ratio.
R = Tyre radius.
VEHICLE PROPULSION POWER:
The vehicle propulsion power is calculated by considering the force acting on the vehicle. Here the hill climbing action is not considered so no hill climbing force.
So the Tractive Force becomes,
`F_te= F_rr+ F_ad`
`F_te=(μ_rr . m .g)+ (0.5 .ρ.A .C_d .v^2`
POWER:
Power is a rate at which work is done, or energy is used. It is equals to amount of work done divided by time it takes to do the work. The unit of power is that Watt (W), which is equals to Joule per sec. (J/sec)
Total power = Total force x Speed
Excel Calculator Screen Shot,
Link for File:https://docs.google.com/spreadsheets/d/1y385yElGaSdhgEzGIIWb2I3W7CisdXb-/edit#gid=312008332
Results:-
Vehicle Propulsion Power = 5.55 KW
Limitations:-
- This power is only required during the vehicle is moving in a plain surface in a constant speed and not in hill regions.
- Also this power is to move the vehicle and the power required during acceleration is different.
III. Assuming that tire pressure reduction by 15 % results in increase of rolling resistance effect by 2 times and evaluate the difference in total traction power keeping all other parameters Same :-
Then the co-efficient of Rolling Resistance becomes,
`μ_(rr )= 0.02`
`μ_(rr )= 0.02*2`
`μ_(rr )= 0.04`
Excel calculator Screen Shot,
Results:-
Difference in Power = 1.94 KW
VI. To Determine the Gradeability the average speed of Range rover Sport Dragon challenge.
The Hybrid SUV completed the previously un-attempted drive that include 99 bends, 999 steps and the slow maneuvering at the bottom of the steps, in a Impressive 22 minutes and 41 seconds.
Link :https://www.youtube.com/watch?v=EUwzWHD3Htg
Vehicle Specification,
- Vehicle-type – PHEV (Plug-in Hybrid Electric Vehicle)
- Maximum Speed – 220 Kmph
Gradeability:
Gradeability of a car is that the ability to climb slop. It is measured in degree or percentage.
Gradeability = `45°`
Average Speed = 40 Kmph
Force acting on car,
- Rolling Resistance Force (`F_rr`).
- Aerodynamic Drag Force (`F_ad`).
- Hill Climbing Force (`F_hc`).
- Linear Acceleration Force (`F_la`).
- Angular Acceleration Force (`F_ω`).
LINK TO THE EXCEL CALCULATOR:-
https://docs.google.com/spreadsheets/d/1y385yElGaSdhgEzGIIWb2I3W7CisdXb-/edit#gid=312008332
REFERRANCE:-