Calculating The Hill Climbing Force Required By a Truck

TARGET:-

1. Finding the hill-climbing force required by a truck.
2. Calculate the required data for the highway.
3. Prepare an excel sheet of the drive cycle
4. Prepare a WOT of GMEV1 car.

OBJECTIVE:-

1. Calculate and compare the hill-climbing power required for a fully loaded and half loaded of tata ultra truck
2. Assum, Plane and Calculate a construction of an NH, keeping in mind about the gradeability minimum length of the highway and considering the summit height will be about 5.5 meters.
3. Prepare a new drive cycle excel file for the model and also include a hill-climbing angle to it and revise the model file “Driver_Glider.slx” 

   •   https://in.mathworks.com/matlabcentral/fileexchange/63823-matlab-and-simulink-racing-lounge-vehicle-modeling

4. Model the WOT (Wide Open Throttle) response of GM EV1 car. Compare it with the official figures for the performance of a real vehicle. Prepare a table showing variation in acceleration time with a 5% change in vehicle parameters. 

EQUATION REQUIRED:-

1. Diameter of the tire-:   $D_t=(2\cdot Hs)+Dr$
2. Angular Velocity-:   $\omega =\frac{v}{r}\cdot G$
3. Rolling Resistance-: $F_{rr}={\mu }_{rr}\cdot m\cdot g$
4. Aerodyanamic Drag Force:- $F_{ad}=0.5\cdot \rho \cdot A\cdot C_d\cdot v^2$
5. Tractive Effort Force:- $Fte=Frr+Fad$
6. Hill Climbing Force:- `F_(HC) = GSW *g * sin(theta)`
7. `G/r *T = (mu_(rr) *m *g) + (0.625 * A * C_d * v^2) + (m+ I*(G^2/eta_g *r^2)* (dv/dt)`

where-

• $D_t$ = Diameter of tire(m).
• $W_s$ = Section Width(m).
• AR = Aspect Ration.
• $H_s$ = Section Height.
• $D_r$ = Rim Diameter(m).
• $\omega$= Angular Velocity(r/s).
• v = Velocity(m/s).
• r = Radius(m).
• G = gear Ratio.
• ${\mu }_{rr}$= Rolling Resistance Co-Efficient`
• m = Mass(kg)
• g = Gravity(m/$s^2$)
• $\rho$ = Air Density(Kg/$m^3$)
• A = Area($m^2$)
• `theta`= Inclination Angle
• $C_d$ = Co-Efficient of Drag
• $F_{te}$ = Traction Effort Force(N)
• $F_{rr}$= Rolling Resistance Force(N)
• $F_{ad}$= Aerodynamic Drag Force(N)
• `F_(HC) =`Hill Climbing Force(N)

THEORY:-

1.  For this experiment i am using a TATA Truck Ultra 1518 and the details are
   •  
2. Gradebility means the ability to climb the slops of any kind of vehicle. Normally it is been calculated for the trucks, if a truck with a gradability of 8% with a speed of 45kmph i.m., the truck can climb the slope rise of 8% at the speed of 45kmph. this is the logical answer of gradability. Keeping in mind the Civil Engineer works with the rise of the highway the run length and the rise/gradability.                  

SOLUTION:-

1. The calculation of the half load and the full load truck is
   • 
2.  The Calculation can be solved using old school technique i.e., Pythagoras theorem. From the above problem we have taken the gradability of that truck which is 20%.

   Gradeability = 20%

   Gradeablity = `tan(alpha)*100`

   Hence,                 'alpha' = 15.21 degree

   therefore,             `sin(alpha) = h/l`

   minimum length (l) = `5.5/sin(15.21)`= 20.69 mtrs

3. from the above link the circuit is given below
   • 
4. The following are the detailes

`G/r *T = (mu_(rr) *m *g) + (0.625 * A * C_d * v^2) + (m+ I*(G^2/eta_g *r^2)* (dv/dt)`

CONCLUSION:-

1. The truck hill climb ratio is 1.4822.
2. The minimum length of the highway 20.69mts.
3. The output is already above.
4. The acceleration time is 14.46667.

   TARGET:-

   1. Finding the hill-climbing force required by a truck.
   2. Calculate the required data for the highway.
   3. Prepare an excel sheet of the drive cycle
   4. Prepare a WOT of GMEV1 car.

   OBJECTIVE:-

   1. Calculate and compare the hill-climbing power required for a fully loaded and half loaded of tata ultra truck
   2. Assum, Plane and Calculate a construction of an NH, keeping in mind about the gradeability minimum length of the highway and considering the summit height will be about 5.5 meters.
   3. Prepare a new drive cycle excel file for the model and also include a hill-climbing angle to it and revise the model file “Driver_Glider.slx” 

      •   https://in.mathworks.com/matlabcentral/fileexchange/63823-matlab-and-simulink-racing-lounge-vehicle-modeling

   4. Model the WOT (Wide Open Throttle) response of GM EV1 car. Compare it with the official figures for the performance of a real vehicle. Prepare a table showing variation in acceleration time with a 5% change in vehicle parameters. 

   EQUATION REQUIRED:-

    

   1. Diameter of the tire-:   $D_t=(2\cdot Hs)+Dr$
   2. Angular Velocity-:   $\omega =\frac{v}{r}\cdot G$
   3. Rolling Resistance-: $F_{rr}={\mu }_{rr}\cdot m\cdot g$
   4. Aerodyanamic Drag Force:- $F_{ad}=0.5\cdot \rho \cdot A\cdot C_d\cdot v^2$
   5. Tractive Effort Force:- $Fte=Frr+Fad$
   6. Hill Climbing Force:- `F_(HC) = GSW *g * sin(theta)`
   7. `G/r *T = (mu_(rr) *m *g) + (0.625 * A * C_d * v^2) + (m+ I*(G^2/eta_g *r^2)* (dv/dt)`

   where-

   • $D_t$ = Diameter of tire(m).
   • $W_s$ = Section Width(m).
   • AR = Aspect Ration.
   • $H_s$ = Section Height.
   • $D_r$ = Rim Diameter(m).
   • $\omega$= Angular Velocity(r/s).
   • v = Velocity(m/s).
   • r = Radius(m).
   • G = gear Ratio.
   • ${\mu }_{rr}$= Rolling Resistance Co-Efficient`
   • m = Mass(kg)
   • g = Gravity(m/$s^2$)
   • $\rho$ = Air Density(Kg/$m^3$)
   • A = Area($m^2$)
   • `theta`= Inclination Angle
   • $C_d$ = Co-Efficient of Drag
   • $F_{te}$ = Traction Effort Force(N)
   • $F_{rr}$= Rolling Resistance Force(N)
   • $F_{ad}$= Aerodynamic Drag Force(N)
   • `F_(HC) =`Hill Climbing Force(N)

   THEORY:-

   1.  For this experiment i am using a TATA Truck Ultra 1518 and the details are
      •  
   2. Gradebility means the ability to climb the slops of any kind of vehicle. Normally it is been calculated for the trucks, if a truck with a gradability of 8% with a speed of 45kmph i.m., the truck can climb the slope rise of 8% at the speed of 45kmph. this is the logical answer of gradability. Keeping in mind the Civil Engineer works with the rise of the highway the run length and the rise/gradability.                  

    

   SOLUTION:-

   1. The calculation of the half load and the full load truck is
      • 
   2.  The Calculation can be solved using old school technique i.e., Pythagoras theorem. From the above problem we have taken the gradability of that truck which is 20%.

      Gradeability = 20%

      Gradeablity = `tan(alpha)*100`

      Hence,                 'alpha' = 15.21 degree

      therefore,             `sin(alpha) = h/l`

      minimum length (l) = `5.5/sin(15.21)`= 20.69 mtrs

   3. from the above link the circuit is given below
      • 
   4. The following are the detailes

   

   `G/r *T = (mu_(rr) *m *g) + (0.625 * A * C_d * v^2) + (m+ I*(G^2/eta_g *r^2)* (dv/dt)`

   Parameters	GM Ev1 calculation	GM Ev1 with 5% increases
   Below Critical Velocity	Torque remains constant but power varies (Constant Trogue Region)  `dv =dT*(3.079-0.000137v^2)`	Torque remains constant but power varies (Constant Trogue Region) `dv =dT*(2.928-0.000137v^2)`
   Below Critical Velocity and Cut-Off Velocity	Torque varies above critical But power remains constant   `dv = dT*((61.512/v)-0.046-(0.000137*v^2))`	Torque varies above critical But power remains constant   `dv = dT*((58.608/v)-0.048-(0.000137*v^2))`

    

   CONCLUSION:-

   1. The truck hill climb ratio is 1.4822.
   2. The minimum length of the highway 20.69mts.
   3. The output is already above.
   4. The acceleration time is 14.46667.