Forces Acting on a Vehicle

AIM:

1. To calculate the maximum speed of the motor used in electric scooter.
2. To calculate the vehicle propulsion power using Excel.
3. To calculate total traction power by varying rolling resistance.
4. To study the gradeability, average speed and forces acting on the range rover sport car.

OBJECTIVE:

1. Calculating speed of the motor by given tire specification, gear ratio and velocity of the vehicle.
2. Calculating vehicle propulsion power by using given input data and proper formula.
3. Calculating total traction power for different rolling resistance and obtain the difference of total traction power.
4. By gone through the video, study the gradeability, average speed and forces acting on the car.

STUDY-1:

Type of forces acting on a vehicle are

1. Rolling Resistance Force.
2. Aerodynamic Drag Force.
3. Acceleration Force.
4. Hill Climbing Force.

Electric scooter:

Electric scooters are plug-in electric vehicles with two or three wheels. The electricity is stored on board in a rechargeable battery, which drives one or more electric motors. Electric scooters have a step-through frame.

Given Data:

Tyre size is 90/100 R10 53J

Speed V=90kmph

Gear Ratio= 7

step 1: convert km/hr to m/sec

As we know that

`1((km)/(hr)) = 1000/3600 m/s`

`= 5/8 m/s`

Then for 90 km/hr,

`= 90*5/18 m/s`

`= 25 m/s`

here,

Width = 90

Aspect Ratio= 100

Rim diameter = R10 inch

Step 1: convert inch into mm

`1 " = 25.4mm`

so,

`D = 10*25.4`

`= 254mm`

To find the Speed of motor Angular velocity

`w = G*v/r (Rad)/s`

Where,

G = gear ratio

r = radius

Step 3: calcuating Tyre Diameter

`dw = 2w ((AR)/100)+d`

Where,

W = width of tyre

AR = Aspect ratio

d = Rim diameter

So,

`dw = 2*90(100/100)+254`

`= 434 mm`

Step 4: calculated the Radius,

`rw = (dw)/2`

`= 434/2`

`= 217mm`

Step 5: convert mm into m for future calculation,

we know that,

1mm=0.001m

Therefore,

=217*0.001

=0.217m

Step 6: Calculate the Angular velocity

`w = G*v/r`

`= 7*((25)/(0.217))`

`= 806.451 (Rad)/s`

Now converting Rad/s to RPM

`= (Rad)/s*60/2*pi`

`= 806.45*(60)/2*3.14`

`= 7701.59 RPM`

Therefore, the maximum speed of the motor is 7701.59 RPM for 90/100 R10 53J used by electric scooter.

For calculation 2:

Tyre size is 90/90 R18 51P

Speed V=90kmph

Gear Ratio= 7

step 1: convert km/hr to m/sec

As we know that

`1((km)/(hr)) = 1000/3600 m/s`

`= 5/8 m/s`

Then for 90 km/hr,

`= 90*5/18 m/s`

`= 25 m/s`

here,

Width = 90

Aspect Ratio= 90

Rim diameter = R18 inch

Step 1: convert inch into mm

`1 " = 25.4mm`

so,

`D = 18*25.4`

`= 457.2mm`

To find the Speed of motor Angular velocity

`w = G*v/r (Rad)/s`

Where,

G = gear ratio

r = radius

Step 3: calcuating Tyre Diameter

`dw = 2w ((AR)/100)+d`

Where,

W = width of tyre

AR = Aspect ratio

d = Rim diameter

So,

`dw = 2*90(90/100)+457.2`

`= 619.2 mm`

Step 4: calculated the Radius,

`rw = (dw)/2`

`= 619.2/2`

`= 309.6 mm`

Step 5: convert mm into m for future calculation,

we know that,

1mm=0.001m

Therefore,

=309.6*0.001

=0.3096m

Step 6: Calculate the Angular velocity

`w = G*v/r`

`= 7*((25)/(0.3096))`

`= 565.24 (Rad)/s`

Now converting Rad/s to RPM

`= (Rad)/s*60/2*pi`

`= 565.24*(60)/2*3.14`

`= 5398 RPM`

Therefore, the maximum speed of the motor is 5398 RPM for 90/90 R18 51P used by electric scooter.

STUDY 2:

Simple excel calculator to identify vehicle propulsion power.

Formula:

• Rolling Resistance (Frr) = μrr* Total Weight

μrr = Coefficient of rolling resistance

• Aerodynamic Drag `Fad = 1/2 rhoAcdV^2 N`

ρ = Air Density

A = Frontal Area

V = Speed

cd= Drag Coefficient

• Total Traction Force `Fte = Frr+Fad N`
• Total power `= ((Fte*V)/1000) kw`

And finally the Total Power of Vehicle A is 35.69Kw and Vehicle B is 43.02Kw.

STUDY 3:

Calculate of difference in total power with 15% reductionin tyre pressure

• In this we can twice the Coefficient of rolling resistance and Rolling Resistance Force.

• Total power difference for Vehicle A is 20.43Kw
• Total power difference for Vehicle B is 32.56Kw

LIMITATION:

• As the mass of the vehicle increases, the motion of the vehicle decreases which inturn the power required to achieve the particular velocity is more.
• The rolling resistance force increases by increasing the coefficient of rolling resistance which depends on the tyre pressure which defines that the force acting on the tyre is more which causes the reduce in velocity.
• Aerodynamic drag fore depends on the coefficient of drag, surface and frontal area which is directly proportional. The drag is less when the surface is smooth than roughened surface which is also called as skin friction.

STUDY 4:

Tianmen Mountain Road in the Hunan Province of China incorporates a dizzying 99 hairpin turns along the 7 miles (11.26 km)of mountainside road. At the summit, this road leads toward 999 steps, all of which lead to Heaven’s Gate, a natural rock arch in the mountainside, mythically thought to be a link between the mortal world and the world of the gods.Reaching Heaven’s Gate is no mean feat. The demanding road that leads up the mountain toward this spectacle is so formidable that there is no room for error. After the road comes the steps, which at their steepest sit at a towering 45-degree angle. While the drive up the 7 miles of winding road has been previously tackled, no vehicle has ever taken on the immense task of driving both the road and the 999 steps all the way to the summit, until now.

Gradeability:

Gradeability is well-defined as the highest grade a vehicle can go up maintaining a particular speed.

To convert, use this angle degrees to the percentage of slope formula.

percentage `% = {tan(degree)}* 100`

For Range Rover Hill Riding an angle of 45 degrees would be.

percentage of slope ={tan(45)⋅100}

Calculated out this gives a slope percentage of 100 %

Gradeability chart

This show the gradeability chart was 45 degrees = 100% and having 1:1 Gradient ratio.

Average Speed of Rang Rover:

Average speed formula,

Speed=DistanceTimeSpeed=DistanceTime

Average speed of Range Rover Sports = 30.14 kmph

Forces Acting on Range Rover Sports During challeges:

• Tractive Force FtFt
• Aerodynamic Force FareoFareo
• Rolling Resistance FrfFrf
• Vertical & Longitudinal Force
• Gradeability Effort

Force acting on the car during hill climbing