Stopping Distance

clear;close all;clc;

g=9.8;                      % standard gravity m/s^2
mu=0.8;                     % coefficient of friction unitless
v=[10:10:100]';             % speed in km/h
tr=1.5*ones(length(v),1);   % reaction time in s

% calculation: flat surface no incline
% reaction distance: speed / reaction time
% braking distance:
% work done to stop the vehicle W=F d
% friction force F=mu m g d => W=mu m g d
% vehicle kinetic energy KE=1/2 m v^2
% W=KE => d=v^2/2/mu/g
rd=v*1000/60/60.*tr;          % reaction distance in m
bd=(v*1000/60/60).^2/2/mu/g;  % braking distance in m
sd=rd+bd;                     % stopping distance in m

% approximation: flat surface no incline
% assuming good and dry road conditions, good tyres and good brakes
% reaction distance: remove the last digit in the speed (km/h),
% multiply by the reaction time and then by 3
% braking distance: remove the zero from the speed (km/h),
% multiply the figure by itself and then multiply by 0.4
aprd=fix(v/10).*tr*3;   % approximate reaction distance in m
apbd=fix(v/10).^2*0.4;  % approximate braking distance in m
apsd=aprd+apbd;         % approximate stopping distance in m

% results
A=[v tr rd aprd bd apbd sd apsd];

% display results using fprintf
fprintf('speed   reaction   reaction       approx reaction   braking        approx braking   stopping       approx stopping\n');
fprintf('(km/h)  time (s)   distance (m)   distance (m)      distance (m)   distance (m)     distance (m)   distance (m)\n');
fprintf('------------------------------------------------------------------------------------------------------------------\n');
fprintf('%3.0f     %2.2f       %5.2f          %5.2f             %5.2f          %5.2f            %5.2f          %5.2f\n', A');

speed   reaction   reaction       approx reaction   braking        approx braking   stopping       approx stopping
(km/h)  time (s)   distance (m)   distance (m)      distance (m)   distance (m)     distance (m)   distance (m)
------------------------------------------------------------------------------------------------------------------
 10     1.50        4.17           4.50              0.49           0.40             4.66           4.90
 20     1.50        8.33           9.00              1.97           1.60            10.30          10.60
 30     1.50       12.50          13.50              4.43           3.60            16.93          17.10
 40     1.50       16.67          18.00              7.87           6.40            24.54          24.40
 50     1.50       20.83          22.50             12.30          10.00            33.14          32.50
 60     1.50       25.00          27.00             17.72          14.40            42.72          41.40
 70     1.50       29.17          31.50             24.11          19.60            53.28          51.10
 80     1.50       33.33          36.00             31.49          25.60            64.83          61.60
 90     1.50       37.50          40.50             39.86          32.40            77.36          72.90
100     1.50       41.67          45.00             49.21          40.00            90.88          85.00

% plot the results
figure;
plot(v,sd,'b-',v,apsd,'ro');
grid on;
xlabel('speed (km/h)');
ylabel('stopping distance (m)');
title('Stopping Distance');
legend('calculated','approximate','location','nw');