# Static Case Study

1. Oct 12, 2008

### ricky_fusion

Hi, My name Ricky, Indonesia. I am newber in this section. So, I am sorry if my question might be wrong location.
1. The problem statement, all variables and given/known data
* The thrust F of each propeller is 1000 lb.
* The thrust directions are described by the angles
α = 10°
β = 5°
γ = 20°
For more detail you can see in : https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=02.3&page=case_intro

Ask : What is the total thrust (force) on the boat in Cartesian components after the driveshaft was bent?

2. Relevant equations
Fx = F sinφ cosθ
Fy = F sinφ sinθ
Fz = F cosφ

3. The attempt at a solution

https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=02.3&page=case_sol

For Normal Force :
F1x = F sinφ1 cosθ1
= 1000 sin90 cos175 = -996.2 lb
F1y = F sinφ1 sinθ1
= 1000 sin90 sin175 = 87.2 lb
F1z = F cosφ1
= 1000 cos90 = 0 lb

Vector F1 can be written in Cartesian notation as

F1 =-996.2i + 87.2j + 0k lb

For Bent Force :
φ' = tan^-1 (tan α cos γ) = 9.41 degree
φ = 90 - φ' = 80.59 degree

θ2 = 200
φ2 = 80.59

F2x = F sinφ2 cosθ2 = -927.0 lb
F2y = F sinφ2 sinθ2 = -337.4 lb
F2z = F cosφ2 = 163.5 lb

Vector F2 can be written in Cartesian notation as

F2 =-927.0i - 337.4j + 163.5k lb

For Total Force :
FT = F1 + F2

= -1923.2i - 250.2j + 163.5k

My question are : (For Bent Force)
1. What is the basic concept to change the degree?
2. Why is the equation/formula should be spherical not just Fx = cos α?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution