Calculations Of Hill Climbing Force

AIM:

To Analysis TATA ULTRA T.12 TRUCK by equating various calculation and observing the ratio of hill climbing power,gradeability, and to create Model the 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 how much can be 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 having third column representing hill climbing angle corresponding to speed and time. Revise the model file “Driver_Glider.slx” such that it can calculate gradient force from drive cycle.
4. Model the WOT (Wide Open Throttle) response of GM EV1 car. Compare it with the official figures of the performance of a real vehicle. Prepare a table showing variation in acceleration time with 5% change in vehicle parameters.

TATA ULTRA T.12 TRUCK:

Tata Motors Limited is India's largest automobile company and a market leader in the Country's commercial vehicles segment. As the world's fifth largest truck manufacturer, Tata Motors has crossed almost seven decades of automotive excellence in a journey marked with significant milestones in excellence and leadership. Using state-of-the-art technology in its world-class manufacturing units, the Company started exporting vehicles in 1961. Since then, Tata Motors has created a name globally, and completed 50 years of its international business in 2011.

Gradient Force From Drive Cycle = 7737N.

STUDY-4:

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

WIDE OPEN THROTTLE:

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.

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 stoichiometeric point.

Given data of a real vehicle,

m = 1540 kg

T max = 140 N m

T = 102000/37 × v = 2756/v

ωc = 733 rad s−1

gear ratio is 11:1, thus G = 11.

m + I = 1638

frontal area A = 1.8 m2

tyre radius is 0.30 m

ηg = 0.95

v = 19.8 m s−1

vmax = 35.8 m s−1

Drag coefficient Cd = 0.19

μrr = 0.0048

Gear ratio = 11

FORMULA USED:

V = rx`omega`/G

G/rT = μrrmg + 0.625ACd ν^2 +(m + IxG^2/ηgr^2)dν/dt

EQUATION DERIVED FROM FORMULA,

dν/dt = 3.11 − 0.000137v^2

dν/dt = 62.1/v−0.046 − 0.000137v^2

vn+1 = vn + δt+(3.11 − 0.000137v^2n)

vn+1 = vn + δt+(62.1/v−0.046 − 0.000137v^2n)

Official figures of the performance of a real vehicle

clear all
close all
clc

t = linspace(0,20,201);
vel=0;
dt = 0.1;
for n = 1:200
    if vel(n)<19.8
        vel(n+1) = vel(n)+dt*(3.11-(0.000137*(vel(n)^2)));
    elseif vel(n)>=35.8
        vel(n+1) = vel(n);
    else
        vel(n+1) = vel(n)+dt*((62.1/vel(n))-0.046-(0.000137*(vel(n)^2)));
    end
end
%   velocity's unit changed to kmph
vel = vel.*3.6;
plot(t,vel)
hold on
%axis([0 30 0 50]);
xlabel('Time/seconds');
ylabel('velocity/kmph');

variation in acceleration time with 5% change in vehicle parameters:

DATA:2

Vehicle mass = 1617 kg

`mu`rr = 0.0048

frontal area A = 1.8 m2

Drag coefficient Cd = 0.19

Tire radius = 0.315

T max = 140 N m

T = 2938.7/v

Gear ratio = 11

`omega` = 733 rad s−1

ηg = 0.95

EQUATION DERIVED FROM FORMULA,

dν/dt = 2.83 − 0.000130v^2

dν/dt = 59.51/v−0.00474 − 0.000130v^2

vn+1 = vn + δt+(2.83 − 0.000130v^2n)

vn+1 = vn + δt+(59.51/vn−0.00474 − 0.000130v^2n)

INPUT PROGRAM:

clear all
close all
clc

t = linspace(0,20,201);
vel=0;
dt = 0.1;
for n = 1:200
    if vel(n)<19.8
        vel(n+1) = vel(n)+dt*(3.11-(0.000137*(vel(n)^2)));
    elseif vel(n)>=35.8
        vel(n+1) = vel(n);
    else
        vel(n+1) = vel(n)+dt*((62.1/vel(n))-0.046-(0.000137*(vel(n)^2)));
    end
end
%   velocity's unit changed to kmph
vel = vel.*3.6;
plot(t,vel)
hold on
%axis([0 30 0 50]);
xlabel('Time/seconds');
ylabel('velocity/kmph');
for n = 1:200
    if vel(n)<20.99
        vel(n+1) = vel(n)+dt*(2.83-(0.000130*(vel(n)^2)));
    elseif vel(n)>=35.8
        vel(n+1) = vel(n);
    else
        vel(n+1) = vel(n)+dt*((59.51/vel(n))-0.00474-(0.000130*(vel(n)^2)));
    end
end
vel = vel.*3.6;
plot(t,vel)
hold on
%axis([0 30 0 50]);
xlabel('Time/seconds');
ylabel('velocity/kmph');
title('Full power(WOT) acceleration of gm electric car');

EXPLANATION OF PROGRAM:

DATA-1

• In this program we want to compare the official figures of the performance of a real vehicle with variation in acceleration time with 5% change in vehicle parameters respect with velocity and time
• To Model the WOT (Wide Open Throttle) response of GM EV1 car. Compare it.
• Data's are obtained from the textbook of real vehicle and the two equations obtained by the formula.
• That equations refers as the critical speed and maximum speed of 'if' ,'else'conditions in MATLAB program.
• To create a program with velocity and time and plot the obtained results on that program it shows the velocity of the vehicle.
• dt value are given by considering the split point of time.
• velocity are converted by multiplying the value of 3.6 in program

DATA-2

• Same process are followed in the data 2 but the changes are made in vehicle parameters as 5%.
• Increment of 5% is acted in the program to compare the actual velocity and time with variation in acceleration time.
• The mass,Tire radius,Frontal area are changed by sum of 5% and equated in the formula.
• Two equations are obtained in that formula and that conditions are used for 'if' 'else' statement in critical speed and maximum speed.
• An critical speed are derived from the formula V = rx`omega`/G and values are initiate in conditions.
• Plot the graph with velocity and time.
• The two velocity's are obtained by the resultant program and that should be varied in time to reached the maximum speed.
• Thus variation in acceleration time with 5% change in vehicle parameters are intiate in graph.

RESULT (GRAPH):

This graphs shows that the vehicle parameters are changed the velocity to attain the top speed will also changed due to time because the mass of vehicle will increase the speed velocity time will also increase.

In this comparison the vehicle parameters are increased by 5% as that time taken for top speed is little varied from actual vehicle time taken.

CONCLUSION:

1. The ratio of hill climbing power = 1.53
2. Minimum length of flyover = 15.8m
3. Gradient Force From Drive Cycle = 7737N.
4. variation in acceleration time with 5% change in vehicle parameters are shown below,

Therefore all the study's are analysis and derived by various calculations.