Wide Open Throttle (WOT) Condition

AIM : To calculate Wide Open Throttle (WOT) Condition.

OBJECTIVES :

1. To find the ratio of hill-climbing power required by fully loaded Tata Ultra truck to the half-loaded one.
2. To calculate the minimum length of the flyover considering the minimum height at the summit should be 5.5 meters.
3. To prepare a new drive cycle excel file for the driver glider model and also include a hill-climbing angle to it.
4. To model the WOT (Wide Open Throttle) response of GM EV1 car and compare it with the official figures of the performance of a real vehicle.
5. To show variation in acceleration time with a 5% change in vehicle parameters.

SOLUTION :

1. To find the ratio of hill-climbing power required by fully loaded Tata Ultra truck to the half-loaded one.

Here, Tata Ultra T.11 model truck is selected for calculations.

The given specifications of the vehicle as shown above are,

Tata Ultra T.11;

CASE – I : Truck is fully loaded

Kerb weight = 3670 kg ;

Payload weight = 7320 kg ;

Gross Vehicle Weight (m) = Kerb weight + Payload weight = 3670 + 7320 = 10990 kg

Gradeability (`theta`) = 28.4% = 16 degrees;

Speed (v) = 30 kmph;

Hill Climbing Force is given by,

F_hc = mgsin(`theta`)

= 10990 x 9.8 x sin(16^o)

= 29686.69 N

F_hc = 29686.69 N;

Power required at full load,

P = F_hc x v

= 29686.69 x 30 x 5 / 18

P = 247389.120 W

CASE – II : Truck is half loaded

Payload weight = 7320/2 = 3660 kg;

Kerb weight = 3670 kg ;

Gross Vehicle Weight (m) = Kerb weight + Payload weight = 3670 + 3660 = 7330 kg;

Gradeability (`theta`) = 28.4% = 16 degrees;

Speed (v) = 30 kmph;

Hill Climbing Force is given by,

F_hc = mgsin(`theta`)

= 7330 x 9.8 x sin(16^o)

= 19800.13 N

F_hc = 19800.13 N;

Power required at half load,

P = F_hc x v

= 19800.13 x 30 x 5 / 18

P = 165001.115 W

Ratio = Power at full load / Power at half load

= `247389.120/165001.115`

= 1.49

The ratio is approximately equal to 1.5 .

2. To calculate the minimum length of the flyover considering the minimum height at the summit should be 5.5 meters.

Here,

Rise or Height = 5.5 meters;

Angle of inclination or Gradeability = 16^o;

Minimum length of flyover;

sin(`theta`) = Rise/Length

`therefore` sin(16^o) = 5.5/(Minimum Length)

`therefore` Minimum Length = sin(16^o)/5.5 = 19.9 m

Minimum Length of the flyover is approximately equal to 20 meters.

3. To prepare a new drive cycle excel file for the driver glider model and also include a hill-climbing angle to it.

The link to Excel sheet data for velocity of a vehicle at a particular time is given below;

https://drive.google.com/file/d/14qdmtW3aM75aKKcNI604nzRufdIAko3p/view?usp=sharing

The velocity of the vehicle in the spreadsheet is converted to m/s from km/hr. The vehicle data is assumed to be for 2 minutes with 1 second gap interval.

Steps to prepare a new drive cycle –

At first, open Matlab and then open ‘DriveCycle’ Excel sheet by double clicking.

Then change the Output Type as ‘Column vectors’. This will select the two columns ‘Time’ and ‘Velocity’ separately. Then click on import data to load the data in the workspace.

Define ‘Drive_Cycle’ as an array of Time and Velocity in command window.

Then open the Driver Glider model file and import ‘Drive_Cycle’ file.

To include hill climbing angle, double click on ‘Glider’ block, the click on ‘Grade Force’ block. Change the value of inclination angle. Here we assumed the value as 15^o.

Then the model is run and we get the graph of ‘Time vs Velocity’ along with the effect of inclination angle.

4. To model the WOT (Wide Open Throttle) response of GM EV1 car and compare it with the official figures of the performance of a real vehicle and to show variation in acceleration time with a 5% change in vehicle parameters.

Governing equation for acceleration time is as follows;

`G/r.T=mu_(rr) mg+0.625AC_d v^2+(m+I(G^2/(eta_g r^2 ))) (dv)/dt`

Parameters assumed are as follows,

m : Mass of vehicle = 1000 kg;

r : Tire radius = 0.30 m;

G : Gear ratio = 11;

v : Velocity of the vehicle = 19.8 m/s;

C_d : Drag Coefficient = 0.19;

`mu_(rr)` : Rolling resistance = 0.0048;

T : Maximum Torque = 140 Nm;

A : Frontal area = 1.8 m²;

`eta_g` : Gear efficiency = 0.95;

dv/dt : Acceleration of vehicle.

CASE – I : Considering original parameters.

%WOT Simulation
clear all
close all
clc

%WOT response for GM EV 1
%Input Data
t = linspace(0,30,301);   %0 to 30s, in 0.1s steps or 301 values
vel = zeros(1,301);       %301 readings of velocity
dt = 0.1;

for n = 1:300
    if vel(n)<19.8
       vel(n+1)=vel(n)+dt*(3.08-(0.000137*(vel(n)^2)));
    else if vel(n)>19.8
            vel(n+1)=vel(n)+dt*((62.1/vel(n))-0.046-(0.000137*(vel(n)^2)));
        end
        if vel(n)>36
           vel(n+1)=vel(n);
        end
    end
end

%Plotting WOT of GM EV1 with original parameters.
vel=vel.*3.6;
figure(1)
plot(t,vel);
axis([0 30 0 140]);
xlabel('Time(sec)');
ylabel('velocity(kmph)');
title('WOT of GM EV1 car');
grid on

Plot –

CASE – II : 5% Change in parameters.

We have,

m : Mass of vehicle = 1050 kg;

A : Frontal area = 1.9 m²;

So,

%WOT response for GM EV1 car varied by 5%.
vel1 = 0
for n = 1:300
    if vel1(n)<19.8
       vel1(n+1)=vel1(n)+dt*(2.95-(0.00013*(vel1(n)^2)));
    else if vel1(n)>19.8
            vel1(n+1)=vel1(n)+dt*((59.14/vel1(n))-0.046-(0.00013*(vel1(n)^2)));
        end
        if vel1(n)>35.8
           vel1(n+1)=vel1(n);
        end
    end
end

%Plotting WOT of GM EV1 with 5% varied parameters.
vel1=vel1.*3.6;
figure(2)
plot(t,vel1);
axis([0 30 0 140]);
xlabel('Time(sec)');
ylabel('velocity(kmph)');
title('WOT of GM EV1 car varied by 5%');
grid on

Plot –

Now we can compare original parameters with 5% varied parameters.

%Comparing Original parameters with 5% varied prameters.
figure(3)
plot(t,vel);
hold on
plot(t,vel1);
axis([0 30 0 140]);
xlabel('Time(sec)');
ylabel('velocity(kmph)');
title('WOT of GM EV1 car Comparison');
legend('Original Parameter','5% variation','Location','southeast')
grid on

Output –

CONCLUSION :

1. The ratio of power required for a fully loaded Tata Ultra truck to half loaded one is approximately equal to 1.5.
2. The minimum length of the flyover with assumed values of gradeability for truck is found to be 20 meters.
3. A new drive cycle is prepared and the driver glider model is simulated including hill climbing angle.
4. The 5% change in vehicle parameters leads to increase of acceleration time.