111710-901-08/07
RSM 400
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4.1.3
Continuous Torque Estimation
The continuous torque, which needs to be smaller or equal to the continuous torque shown in chapter 3, can
be estimated using the following formulas:
Formula
Symb.
Unit
Description
𝑀
𝑐𝑜𝑛𝑡
= 𝑀
𝐼
+ 𝑀
𝐴
+ 𝑀
𝑊
+ 𝑀
𝑠𝑡𝑎𝑡
𝑀
𝐼
Nm
Torque caused by the payload’s inertia
and vehicle motion
𝑀
𝐴
Nm
Torque caused by lateral accelerations
𝑀
𝑊
Nm
Torque caused by wind force of the pay-
load
𝑀
𝑠𝑡𝑎𝑡
Nm
Torque caused by horizontal CoG offset
of the payload
–
to be avoided!
𝑀
𝐼
= 𝐹
𝐼
∙ 𝐶𝑜𝐺
= 𝐽 ∙ 𝜑̈ ∙
𝜋
180
= 𝑚 ∙ 𝐶𝑜𝐺
2
∙ 𝜑̈ ∙
𝜋
180
𝐽
kg
m
2
Payload moment of inertia
𝑚
kg
Payload point mass
𝐶𝑜𝐺
m
Vertical
offset between the payload’s cen-
ter of gravity and the stabilization Mount’s
pivot
𝜑̈
deg/s
2
Angular acceleration
𝑀
𝐴
= 𝐹
𝐴
∙ 𝐶𝑜𝐺
= (𝜑̈ ∙
𝜋
180
∙ ℎ + √𝑥̈
2
+ 𝑦̈
2
) ∙ 𝑚 ∙ 𝐶𝑜𝐺
ℎ
m
Vertical distance between the vehicle’s
pivot and the payload CoG
𝜑̈
deg/s
2
Angular acceleration
𝑥̈
m/s
2
Lateral acceleration- x-direction
𝑦̈
m/s
2
Lateral acceleration- y-direction
𝑀
𝑊
= 𝐹
𝑊
∙ 𝐶𝑜𝐺
= 𝐴
𝑊
∙ 𝑐
𝑊
∙
𝜌
𝐿
2
∙ 𝑣
𝑊
2
∙ 𝐶𝑜𝐺
𝐴
𝑊
m
2
Surface area of the payload caught by the
wind
𝑐
𝑊
m
2
Drag coefficient of the payload (the geo-
metric form may be simplified)
𝜌
𝐿
kg/m
3
Air density
𝑣
𝑊
m/s
Wind speed
𝑀
𝑠𝑡𝑎𝑡
= 𝐹
𝑠𝑡𝑎𝑡
∙ 𝑟
= 𝑚 ∙ 𝑔 ∙ √𝑥
2
+ 𝑦
2
𝑔
m/s
2
Gravitational acceleration
–
9.81 m/s
2
𝑥
m
Horizontal offset between payload CoG
and center of stabilization Mount’s sur-
face
–
x-direction
𝑦
m
Horizontal offset between payload CoG
and center of stabilization Mount’s sur-
face
–
y-direction
