aim: to find the force in [N], torque in [Nm] and power in [kW ] 

aim: to find the force in [N], torque in [Nm] and power in [kW ]

Q1) Consider a vehicle and trailer having the following parameters:

Using the above values, calculate, the force in [N], torque in [Nm] and power in [kW] requirement at the wheel as a function of vehicle speed in [kmph] for the following scenarios:

a. No acceleration, flat ground, no headwind, no trailer
b. No acceleration, 7% grade, no headwind, with trailer
c. Acceleration of 0.2g, no grade, headwind of 5 kmph in the vehicle direction, no trailer

This will give an idea of power and torque requirements for a typical vehicle for different driving conditions.

Show sample calculations for 50 kmph, tabulate the force components, total force, along with total torque and power for 25, 50, 75, 100, 125 kmph, and plot the total power and torque requirements for all 3 scenarios as a function of speed (0 to 150 kmph). Use Matlab for calculations and plotting.

Comment on the results, comparing the differences and outlining certain observations.

Note: For calculating rolling radius, assume rolling radius to be 97% of the tire calculated radius, due to tire compression. For case with trailer, only consider the aerodynamic drag of the trailer, as it has much
larger projected area and higher drag coefficient.

solution:

FORMULA USED

][1] FORCE= rolling resistance force + areodynamic force + grading force

WHERE,

[2]TORQUE= FORCE * WHEEL RADIUS

NOTE{THE TIRE RADIUS IS TAKEN IN MM} IN MY CODES.

for calculating wheel radius

[3] POWER = FORCE * VELOCITY

clear all
close all
clc
% tire size [245/60R18]
AR=60;
W=245;
D=18*25.4;
% gravity
g=9.81;
% vehical weight[kg]
m=2400;
% drag coefficient
cd=0.35;
%frontal area [m^2]
af=2.4;
% air density[kg/m^2]
rho=1.225;
% rolling resistance coefficient
cr=0.013;
% tire size 245/60R18
% trailer frontal area[m^2] 
af_t=5;
% trailer drag coefficient
cd_t=0.8;
% trailer weight [kg]
mt=1250;
% vehical velocity [km/h]
velocity=[0,25,50,75,100,125,150];

%% a. No acceleration, flat ground, no headwind, no trailer
% rolling resistance force
frr1=cr*m*g*cosd(0);
% areodynamic force
fad1=0.5*rho*af*cd*(velocity).^2;
% grading force 
fhc1=m*g*sind(0);
% load
force1=frr1+fad1
% torque
torque1= force1*WHEELRADIUS(W,AR,D)
% power 
power1=force1.*velocity
%% b. No acceleration, 7% grade, no headwind, with trailer
% rolling resistance force
frr2=cr*m*g*cosd(3.15);
% areodynamic force
fad2=0.5*rho*af*cd*(velocity).^2;
% grading force 
fhc2=m*g*sind(3.15);
% areodynamic force for trailer
fad_trailer=0.5*rho*af_t*cd_t*(velocity).^2;
% load with trailer
force2=frr2+fad2+fhc2+fad_trailer
% torque with trailer
torque2= force2*WHEELRADIUS(W,AR,D)
% power with trailer
power2=force2.*velocity
%% c. Acceleration of 0.2g, no grade, headwind of 5 kmph in the vehicle direction, no trailer
% rolling resistance force
frr3=cr*m*g*cosd(0);
% areodynamic force
fad3=0.5*rho*af*cd*(velocity+5).^2;
% grading force 
fhc3=m*g*sind(0);
% load
force3=frr3+fad3+fhc3+m*(0.2*g)
% torque
torque3= force3*WHEELRADIUS(W,AR,D)
% power 
power3=force3.*(velocity+5)

%% plotting 
figure(1)
plot(velocity,torque1,"r","LineWidth",3)
hold on
plot(velocity,torque2,"b","LineWidth",3)
plot(velocity,torque3,"g","LineWidth",3)
legend('A','B','C')
xlabel('VELOCITY')
ylabel('TORQUE')
title('VELOCITY VS TORQUE')
grid on
figure(2)
plot(velocity,power1,"r","LineWidth",3)
hold on
plot(velocity,power2,"b","LineWidth",3)
plot(velocity,power3,"g","LineWidth",3)
legend('A','B','C')
xlabel('VELOCITY')
title('VELOCITY VS POWER')
ylabel('POWER')
grid on

function for CALCULATION WHEEL RADIUS

function [rw]=WHEELRADIUS(W,AR,D)
% tire size [245/60R18]
H=(AR*W)/100;           % TIRE HIGHT
dw=D+2*H;               % WHEEL DIAMETER
rw=(dw/2);              % RADIUS OF WHEEL (WHERE O.97=GIVEN CONDITION)
end

NOTE { I TOOK RADIUS IN MM , DRAG COEFFICIENT IS NOT TAKEN IN FORMULA LIST BUT I TOOK IT DUE TO QUESTION.

Only consider the aerodynamic drag of the trailer, as it has much}

REFRENCES:

https://skill-lync.com/knowledgebase/important-formulae-for-development-of-hybrid-drives

https://x-engineer.org/calculate-wheel-radius/

thank you