Istanbul Technical University, Mechanical Engineering Department
Instructor: Prof. Dr. Özgen Akalin
MAK 4053E VEHICLE TECHNOLOGY
HOMEWORK - 2
Due: November 15, 2024
1) Calculate the maximum grade this FWD vehicle can climb while towing a boat.
a) Draw free-body-diagrams (FBD) for the car and the boat separately.
b) Derive the expressions for the maximum grade your vehicle can climb while towing the
boat trailer without wheel slippage (traction limited gradability)
(In the analysis it is reasonable to neglect the longitudinal acceleration and aerodynamic
resistances. Assume suspension is rigid, i.e. no suspension travel)
c) Repeat part b for a 4WD vehicle with an interaxial drive where the torque is distributed
to the front and rear axles equally.
d) Compare FWD and 4WD vehicles in term of gradeability using a graph. Plot maximum
grade (%) with respect to coefficient of road adhesion μP.
L: Car Wheelbase ; Lt: Trailer wheelbase; fR= Rolling resistance coefficient (0.015)
W: Car weight [N] = 8 x L [mm]; Location of towing hitch d= L/3; s=h/2;
G: Trailer weight [N] = W / 4; ht= 0.8 x h; l3= l1; l4= l1 / 2; (see student data sheet for the
vehicle data)
Istanbul Technical University, Mechanical Engineering Department
Instructor: Prof. Dr. Özgen Akalin
2) A FWD passenger car has a weight of (laden) 20000 N and equipped with an engine
having torque speed characteristics (Full-load) as shown in the figure below. This vehicle
has a wheelbase of 2810 mm. The center of gravity is 1349 mm behind the front axle and
702 mm above the ground level. The width of this vehicle is 1811 mm, unloaded height is
1429 m and aerodynamic drag coefficient CD is 0.32. The coefficient of rolling resistance
of tire on dry asphalt road is given by fR=0.015. Assume the transmission efficiency is 98
% in the direct drive and 95 % in other gears and in the axle drive. You may neglect the
tire slip and the inertia of the drive train components. Frontal area of the vehicle can be
calculated as; vehicle width x height.
a) Plot the engine torque and engine power with respect to engine speed. (Show axes and
labels. Do not use separate graphs)
b) Select a proper tire size for this vehicle from the table below.
c) Plot the power required to overcome vehicle road resistances on a level road w.r.t. road
speed.
d) Calculate the maximum speed this vehicle can reach on a level road.
e) Calculate the maximum grade this vehicle can climb without wheel slippage on a dry
pavement where the traction coefficient is 0.8.
f) Using the conventional methods shown in the class, calculate the axle drive
(differential) and manual transmission gear ratios of a matching 5 speed manual
transmission. Assume the 4th speed is direct-drive and 5th speed is reserved for fuel
economy. Use geometric progression rule to calculate the intermediate gear ratios (i.e.
2nd, 3rd speed gear ratios).
g) Select an economy gear ratio (5th gear ratio) that will give best fuel consumption while
cruising on a highway at a constant speed of 110 km/h.
h) Plot the tractive effort w.r.t. the vehicle speed and tractive power (power at wheels)
w.r.t. vehicle speed for all gear ratios.
i) What is the maximum speed this vehicle can reach on a 10 % slope? Use the graphs
you plotted in section “h” to answer this question. Which gear should be used to reach
this speed?
Istanbul Technical University, Mechanical Engineering Department
Instructor: Prof. Dr. Özgen Akalin
Istanbul Technical University, Mechanical Engineering Department
Instructor: Assoc. Prof. Dr. Özgen Akalın
4
Istanbul Technical University, Mechanical Engineering Department
Instructor: Assoc. Prof. Dr. Özgen Akalın
1. (*) See student data on Ninova
2. Graphs will be plotted using computer graphics. No hand drawn graph is accepted! Show legends, labels and
units.
3. All homework assignments will be submitted through Ninova.
4. No late homework is accepted.
