function force = resistance_force (vel_ms, slope)

%RESISTANCE_FORCE Determines the air, tire, and gravity resistance force
%   FORCE = RESISTANCE_FORCE (VEL_MS, SLOPE) computes the total resistance
%   force due to air and tire resistance and gravity for a car running at a
%   velocity of VEL_MS and up a slope of SLOPE %.
%
%   Inputs:
%      VEL_MS: a vector of car velocities expressed in [m/s]
%      SLOPE:  a scalar containing the slope of the road surface in [%]
%
%   Outputs:
%      FORCE: a vector of resistance forces expressed in [N].  FORCE has
%      the same dimensions as VEL_MS.
%  
%
%   Assumptions: 
%         - the air resistance is proportional to the velocity squared
%         - the rolling friction is proportional to the weight of the car
%         - there is no wind
%         - the slope is constant
%         - the car characteristics correspond approximately to those of a
%           Ford Taurus

%%
%% ME 2016
%% Fall 2007
%%
%% AUTHOR:  Chris Paredis
%%


% define the constants
g = 9.81;                        % gravitational constant in [m/s2]
air_density = 1.29;              % [kg/m3]

% define the car parameters
mass = 1650;                     % [kg]
drag_coefficient = 0.32;         % dimensionless
frontal_area = 2.2;              % [m2]
rolling_coefficient = 0.009;     % dimensionless
slope_rad = atan(slope/100);     % slope in radians

% compute drag force (wind and rolling): in [N]
wind_resistance = 0.5*drag_coefficient*frontal_area*air_density * vel_ms.^2;
rolling_resistance = (rolling_coefficient * mass * g * cos(slope_rad))*sign(vel_ms); 
gravity_resistance = mass*g*sin(slope_rad);

% total resistance
force = wind_resistance + rolling_resistance + gravity_resistance;

return;