Analysis of various Forces acting on a truck and Simulation model of WOT (Wide Open Throttle) response of GM EV1 car using MATLAB & Simulink.

Aim: To analyze truck by equating various calculations and observing the ratio of hill-climbing power, gradeability, and creating the Model of WOT (Wide Open Throttle) response of GM EV1 car.

Objective:

1. To find the ratio of hill-climbing power required by fully loaded tata ultra truck to the half-loaded one
2. To find minimum height length for a flyover which is planned to be constructed on a national highway. Keeping in mind about the gradeability for trucks, considering the minimum height at the summit should be 5.5 meters along with assumptions. 
3. To prepare a new drive cycle to excel file for the model and also include a hill-climbing angle to it. Revise the model “Driver_Glider.slx” file.
4. To 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.  

Theory:

• Wide-open throttle (WOT) refers to an internal combustion engine's maximum intake of air and fuel that occurs when the throttle plates inside the carburetor or throttle body are "wide open", providing the least resistance to the incoming air. In the case of an automobile, WOT is when the accelerator is depressed fully, sometimes referred to as "flooring it.
• In the case of a diesel engine, which does not have a throttle valve, WOT is the point at which the maximum amount of fuel is being injected relative to the amount of air pumped by the engine, generally in order to bring the fuel-air mixture up to the stoichiometric point. If any more fuel were to be injected then black smoke would result.
• At wide-open throttle, manifold vacuum decreases. The higher manifold pressure in turn allows more air to enter the combustion cylinders, and thus additional fuel is required to balance the combustion reaction. The additional air and fuel reacting together produce more power.

1) To find the ratio of hill-climbing power required by fully loaded tata ultra truck to the half-loaded one

• The data is taken from https://light-trucks.tatamotors.com/light-trucks/tata-ultra/specifications/tata-ultra-t-12-light-trucks-specifications.aspx

Full loaded truck:

1. GVW = Kerb weight + Payload = 3735 + 8255 = 11990 kg
2. Acceleration due to gravity = 9.8 m/s^2
3. Gradeability = 25.6% = 15deg
4. Force =  = 11990.9.8.sin(15) = 76411.55 N
5. Total power = force*speed
6. Speed = 25kmph = 25*5/18 = 6.94 ~ 7
7. Power = 76411.55*7 = 534880.85 W

Half loaded truck:

1. GVW = Kerb weight + Payload/2 = 3735 + 8255/2 = 7862.5 kg
2. Acceleration due to gravity = 9.8 m/s^2
3. Gradeability = 25.6% = 15deg
4. Force =  = 7862.5*9.8*sin(15) = 50107.241 N
5. Total power = force*speed
6. Speed = 25kmph = 25*5/18 = 6.94 ~ 7
7. Power = 50107.241*7 = 350750.687 W

So we get,

• Power ratio = full load power/half load power = 534880.85/350750.687 = 1.52

2) To find minimum height length for a flyover which is planned to be constructed on a national highway. Keeping in mind about the gradeability for trucks, considering the minimum height at the summit should be  5.5 meters along with assumptions. 

Given:

Minimum height = 5.5m

Gradeability = 25.6% = 15 deg

From the fig,

sin(θ)=opp/hyp

So,

0.258 = 5.5/hyp

hyp = 21.3m = minimum length of flyover

Now,

Using Pythagoras theorem,

where,

a = 5.5m, c = 21.3m

we get,

b = 15.8m = minimum run of flyover

Total run of flyover = 31.6m

3) To prepare a new drive cycle to excel file for the model and also include a hill-climbing angle to it and revise the model “Driver_Glider.slx” file.

• First, download the driver glider file from https://in.mathworks.com/matlabcentral/fileexchange/63823-matlab-and-simulink-racing-lounge-vehicle-modeling
• Now, open the model using the instructions provided from https://skill-lync.freshdesk.com/support/solutions/articles/43000576806-how-to-open-driver-glider-model-in-simulink

Main Model:

• The drive cycle data is given as input for the model.

Driver Model:

Glider Model:

Output:

4) To 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.

The General Motors EV1 was an electric car produced and leased by General Motors from 1996 to 1999. It was the first mass-produced and purpose-designed electric vehicle of the modern era from a major automaker and the first GM car designed to be an electric vehicle from the outset.

Specifications:

Case 1 - Original Parameters:

Data:

• Drag coefficient = Cd = 0.19
• Motor speed = 12000 rpm
• Frontal area = A = 1.8 m^2
• Rolling resistance =  = 0.0048
• Efficiency = 95%
• Gross weight = m+l = 1540 kg
• Tire radius = r = 0.3 m
• Gear ratio = G = 11
• Motor torque = Tmax = 140 Nm
• Velocity = v = 19.8 m/s
• Angular speed = 733 rad/s
• Power = 102 kW
• Air density = 1.25 kg/m^3
• Limiting acceleration velocity = vmax = 35.8 m/s

Formulae Used:

• dv/dt = 3.11-0.000137.v^2
• dv/dt = 62.1/v-0.046-0.0000137.v^2
• vn+1 = vn+$\delta$t+(3.11-0.000137.v^2n)
• vn+1 = vn+$\delta$t+(62.1/v-0.046-0.000137v^2n)

MATLAB Code:

clear all
close all
clc
 
% Original Parameters of GM EV1 Car

t = linspace(0,50,201);

% Velocity Array - (Defining before calculation
v = zeros(1,201);
 
% Differentiation time - dt (t = 0.1 s)
dt = 0.1;
 
% Loop for velocity and distance calculation
for i = 1:200
    if v(i)<19.8 % (w(omega) = 10.8 rad/s after Critical Speed)
        v(i+1) = v(i) + dt*(3.11-(0.000137*(v(i)^2)));
    elseif v(i)>=35.8
        v(i+1) = v(i);
    else
        v(i+1) = v(i) + dt*(((62.1)/v(i))-0.046-(0.000137*(v(i)^2)));
end
end

% Converting the velocity from (m/s) to Kmph
v = v.*3.6;

% Plotting the time vs velocity graph
plot(t,v,'linewidth',1.5,'color','r');

grid on

xlabel('Time (s)')
ylabel('Velocity (Kmph)')

title('WOT (Wide Open Throttle) of GM EV1 Car')

Graph:

Case 2 - 5% Change in Vehicle Parameters:

Data:

• Drag coefficient = Cd = 0.19
• Motor speed = 12000 rpm
• Frontal area = A = 1.8 m^2
• Rolling resistance =  = 0.0048
• Efficiency = 95%
• Gross weight = m+l = 1617 kg
• Tire radius = r = 0.3 m
• Gear ratio = G = 11
• Motor torque = Tmax = 140 Nm
• Velocity = v = 19.8 m/s
• Angular speed = 733 rad/s
• Power = 102 kW
• Air density = 1.25 kg/m^3
• Limiting acceleration velocity = vmax = 35.8 m/s

Formulae Used:

• dv/dt = 3.23-0.000152.v^2
• vn+1 = vn+$\delta$t+(3.23-0.000152.v^2n)
• vn+1 = vn+$\delta$t+(64.77/v-0.048-0.000152v^2n)

MATLAB Code:

clear all
close all
clc
 
% 5% change in parameters of GM EV1 Car

t1 = linspace(0,50,201);

% Velocity Array - (Defining before calculation
v1 = zeros(1,201);
 
% Differentiation time - dt (t = 0.1 s)
dt1= 0.1;
 
% Loop for velocity and distance calculation
for j = 1:200
    if v1(j)<20.49 % (w(omega) = 10.8 rad/s after Critical Speed)
        v1(j+1) = v1(j) + dt1*(3.23-(0.000152*(v1(j)^2)));
    elseif v1(j)>=37.59
        v1(j+1) = v1(j);
    else
        v1(j+1) = v1(j) + dt1*(((64.77)/v1(j))-0.048-(0.000152*(v1(j)^2)));
end
end

% Converting the velocity from (m/s) to Kmph
v1 = v1.*3.6;

% Plotting the time vs velocity graph
plot(t1,v1,'linewidth',1.5,'color','b');

grid on

xlabel('Time (s)')
ylabel('Velocity (Kmph)')

title('WOT (Wide Open Throttle) of GM EV1 Car')

Graph:

Case 1 & Case 2 combined:

MATLAB Code:

clear all
close all
clc
 
% Original Parameters of GM EV1 Car

t = linspace(0,50,201);

% Velocity Array - (Defining before calculation
v = zeros(1,201);
 
% Differentiation time - dt (t = 0.1 s)
dt = 0.1;
 
% Loop for velocity and distance calculation
for i = 1:200
    if v(i)<19.8 % (w(omega) = 10.8 rad/s after Critical Speed)
        v(i+1) = v(i) + dt*(3.11-(0.000137*(v(i)^2)));
    elseif v(i)>=35.8
        v(i+1) = v(i);
    else
        v(i+1) = v(i) + dt*(((62.1)/v(i))-0.046-(0.000137*(v(i)^2)));
end
end

% Converting the velocity from (m/s) to Kmph
v = v.*3.6;

% 5% change in parameters of GM EV1 Car

t1 = linspace(0,50,201);

% Velocity Array - (Defining before calculation
v1 = zeros(1,201);
 
% Differentiation time - dt (t = 0.1 s)
dt1= 0.1;
 
% Loop for velocity and distance calculation
for j = 1:200
    if v1(j)<20.49 % (w(omega) = 10.8 rad/s after Critical Speed)
        v1(j+1) = v1(j) + dt1*(3.23-(0.000152*(v1(j)^2)));
    elseif v1(j)>=37.59
        v1(j+1) = v1(j);
    else
        v1(j+1) = v1(j) + dt1*(((64.77)/v1(j))-0.048-(0.000152*(v1(j)^2)));
end
end

% Converting the velocity from (m/s) to Kmph
v1 = v1.*3.6;

% Plotting the time vs velocity graph
plot(t,v,'linewidth',1.5,'color','r');
hold on
plot(t1,v1,'linewidth',1.5,'color','b');

grid on

xlabel('Time (s)')
ylabel('Velocity (Kmph)')

title('WOT (Wide Open Throttle) of GM EV1 Car')

legend('Original Parameters','5% change in Parameters','location','northwest')

Graph:

Result & Conclusion:

• The ratio of hill-climbing power = 1.52
• Minimum length of flyover = 15.8 m
• Original Parameters = 128.79 kmph
• 5% change in Vehicle Parameters = 135.28 kmph

Therefore all the objectives are performed successfully using MATLAB & Simulink.