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[Illustration: Fig. 8]

=Effect of Grades.=--Grades increase or decrease the resistance to
translation due to the fact that there is a component of the weight of
the vehicles parallel to the road surface and opposite in direction to
the motion when the load is ascending the hill and in the same
direction when the vehicle is descending. In Fig. 8 _W_ represents the
weight of the vehicle, acting vertically downward, _w_ is the
component of the weight perpendicular to the road surface and _W_{2}_
is the component parallel to the road surface.

_W_{2}_ = _W_ tan _THETA_.

tan _THETA_ = 0.01 x per cent of grade.

_W_{2}_ = 0.01 _W_ x per cent grade.

_W_{2}_ = 0.01 x 2000 x per cent of grade, for each ton
of weight of vehicle.

Hence _W_{2}_ = 20 lbs. per ton of load for each one per cent of
grade.

The gravity force acting upon a vehicle parallel to the surface on a
grade is therefore 20 lbs. per ton for each one per cent of grade and
this force tends either to retard or to accelerate the movement of the
vehicle.

Let _F_ = the sum of all forces opposing the translation of a vehicle.

_F = f_{r} + f_{i} + f_{p} + f_{a} + f_{g}_ (1)

where

_f_{r}_ = rolling resistance of road surface.
_f_{i}_ = resistance due to internal friction in the vehicle.
_f_{p}_ = resistance due to impact of the road surface.
_f_{a}_ = resistance due to air.
_f_{g}_ = resistance due to grade, which is positive when
ascending and negative when descending.

All of the above in pounds per ton of 2000 lbs.

Let _T_ = the tractive effort applied to the vehicle by any means.

_T_ >= must be greater than _F_ in order to move the vehicle.

By an inspection of (1), it will be seen that for a given vehicle and
any type of road surface, all terms are constant except _f_{a}_ and
_f_{g}_. _f_{a}_ varies as the speed of the vehicle and the driver can
materially decrease _f_{a}_ by reducing speed. _f_{g}_ varies with the
rate of grade. For any vehicle loaded for satisfactory operation on a
level road with the power available, the limiting condition is the
factor _f_{g}_. If the load is such as barely to permit motion on a
level road, any hill will stall the vehicle. Therefore, in practice
the load is always so adjusted that there is an excess of power on a
level road. If draft animals are em