The Height above Ground of CG (h):
The weight of the rear axle (Wr1) will be weighed while the front pair of wheels are
raised up quite a small distance H (or h1) (as shown in figure 2).
| Fig.1 Measure the rear axle weight (Wr1) and the distance of front raise (H) |
| Fig. 2 The front wheels are raised up a small distance H (h1), r is the wheel radius, (h is the unknown distance of the CG height) |
Using Fig. 2:
The summation of vertical forces in the y direction is equal 0.
Σ F
y = 0
Rf1 + Rr1 – W = 0
Then: Rf1 = W – Rr1
The summation of moments about any point is equal 0, then:
Σ MA = 0
Rf 1 (L cos θ) – W (AB) = 0
Rf 1 (L cos θ) = W (AB) ……………………………….(1)
From the figure 2:
AB = AC – BC,
Where:
AC = b cos θ, and
BC = ED = (h-r) sin θ,
Then:
AB = AC – BC = b cos θ – (h-r) sin θ
Substitute the value of AB form the above equation in Eq. (1), then
Rf1 (L cos θ) = W (b cos θ – (h-r) sin θ)
Rf1 (L cos θ) = W b cos θ – W (h-r) sin θ
W (h-r) sin θ = W b cos θ – Rf1 (L cos θ)
h– r = [b – L (Rf1/W)] cot θ …………………………..(2)
h = [b – L (Rf1/W)] cot θ + r ………………………….(3)
(Note: if the rear wheels are lifted, the b should be changed to a and the value Rfl be changed
to Rrl)
where:
θ = sin-1 (H/L)
(h-r) is the distance of CG above the axle plane, Eq. (2)
h is the distance of CG above the ground, Eq. (3)
* In Eq. 3, the units of Rf1 and W both can be expressed in unit force (N, lb) or unit mass
(kg), the units of b, L, r and h can be expressed in (m, cm, mm, or ft, in).
An Excel program can be found on unilearn assignment.