Highways and Highway TransportationChatburn, George R.
History
Highways and Highway Transportation
Chatburn, George R.
Roads; Transportation
_P_
_L_ = -------, (3)
μ + _g_
where _L_ = weight of load drawn, including weight of vehicle
(subtract weight of vehicle for net load);
_H_ = weight of horse;
_T_ = weight of tractor;
_P_ = effective tractive force exerted (available engine
effort);
μ = coefficient of road resistance;
_g_ = grade (gradient) = tangent of angle of incline, nearly the
same for small angles as the sine of the angle of incline,
that is, the height of the incline divided by its length;
_t_ = the direct pull of the horse divided by the weight of the
horse;
_h_ = horse-power = work of 33,000 ft.-lb. per minute.
_v_ = velocity in miles per hour.
Equation (3) indicates that the load, including its own weight, that
a truck or an automobile can draw varies directly as the horse-power
exerted effectively, and inversely as the velocity. Also it decreases
as the coefficient of road resistance, μ, and the gradient _g_
increases.
The resistance coefficient, μ may include axle or internal resistance
of the vehicle plus road surface resistance plus air resistance. The
axle resistance is nearly a constant, the road resistance likewise, but
the air resistance depends upon the speed _v_, varying approximately as
the square of the velocity. W. S. James, in the _Journal of the Society
of Automotive Engineers_, June, 1921, uses the formula
_F_ = _CAV_²
where _F_ = the wind force in pounds;
_C_ = a constant, varies from .003 to .004;
_A_ = frontal area of automobile in square feet
approximately 26;
_V_ = velocity in miles per hour.
His researches show that the available engine effort _P_ of equation
(3) or horse power _h_ is not quite constant but varies with the speed.
His table follows:
---------+-----------------------+---------------------------
|Available Engine Effort|
Car Speed| Per 1000 lb. of Car |Air Resistance Per 1000 lb.
m.p.h. | Weight, Lbs. | of Car Weight, Lbs.
---------+-----------------------+---------------------------
15 | 107.3 | 4.9
16 | 105.2 | 6.8
20 | 107.6 | 8.8
25 | 106.0 | 13.4
30 | 103.9 | 19.2
35 | 101.2 | 26.0
40 | 98.0 | 34.1
45 | 94.1 | 43.4
50 | 86.8 | 53.8
---------+-----------------------+---------------------------
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