Devin Bunce
Detailed Design Analysis
Design Overview:
1. Change in Impulse
a. On Board Spool
i. Purpose: Mitigate impulse on plane when full tension is obtained. Method
consisted of a servo pressing a high friction material against the edge of the
spool to slow down its rotation to a stop.
ii. Status: Energy analysis is set up however it does not include energy being added
to the system from lift. 75% Complete.
iii. Next Action: Consult Mario about how to include lift into dynamic analysis.
Write up equations into a Matlab script to allow easy fine tuning.
2. Fuselage Impact Analysis
a. Spring Constant of EPP Foam
i. Purpose: Use foam as a way to mitigate crash impulse and reduce the amount
of damage it takes at high velocity impacts.
ii. Status: Conducted a test plan to load a block of foam with varying weights and
measure the deflection to acquire an approximate constant K.
iii. Next Action: Confirm method of measuring deflections and find significant
enough weights to adequately deflect foam.
b. Impact Loading
i. Purpose: Find stresses fuselage perceives during impact to verify 3D printed
internal structure feasibility.
ii. Status: Force equations are complete.
iii. Next Action: Complete pressure vessel stress analysis. Get material parameters
from 3D printing lab. Conduct spring constant experiment.
3. Wing Loading
i. Purpose: Validate dimensions of carbon fiber spars to minimize the amount of
material used while maintaining a structural integrity for a factor of safety.
ii. Status: Derived distributed load for lift across the wing.
iii. Next Action: Write equations in Matlab code to make fine adjustments easy to
check and allow for smooth refinements.
4. Additional Topics for Weeks 9-12
a. 3D Printed Fuselage Feasibility
b. Additional Static Loading of Fuselage
c. Work with team on CAD Model
Technical Appendix:
1. Change in Impulse
a. ∆𝐾𝐸 + ∆𝑃𝐸 = 𝑊𝑛𝑐 ; Where ∆𝑃𝐸 = 0
b.
c.
1
1
𝐼𝑤𝑖 2 − 2 𝐼𝑤𝑓 2 =
2
1
𝑉
𝐼(
)2 = 𝐹𝑓 𝑠;
2 𝑟𝑠𝑝𝑜𝑜𝑙
∫ 𝐹 ∙ 𝑑𝑠; Where the final angular velocity is zero
Where s is the total distance the frictional pad is in contact with the
spool. V is the velocity of the plane during steady flight (Assumed to be 30 mi/hr).
1
d. 𝐼 = 2 𝑚𝑟𝑠𝑝𝑜𝑜𝑙 2 ; Here it is assumed that the spool (thread included) behaves like a solid
cylinder.
e. From hear approximate values need to be used and Lift needs to be added to the
analysis. However, conceptual check, if s goes to infinity, the amount of force required
to slow system goes to zero which makes engineering sense.
2. Fuselage Impact Analysis
a. 𝐹 = 𝑘∆𝑥; Where k is the spring constant.
𝑑𝑣
b. 𝐹 = 𝑚 𝑑𝑡 = 𝑘𝑥
𝑑𝑣 𝑑𝑥
𝑚 𝑑𝑡 𝑑𝑥 = 𝑘𝑥
𝑚𝑉𝑑𝑉 = 𝑘𝑥𝑑𝑥
1
1
𝑚(𝑉𝑓 − 𝑉𝑖 ) = 2 𝑘(𝑥𝑓 2 − 𝑥𝑖 2 ); Where final velocity and initial x are zero.
2
𝑚𝑉𝑖 2
𝑘
𝑥𝑓 = √
∴ 𝐹 = 𝑘𝑥𝑓
From here the force analysis needs to be applied to a pressure vessel (the approximate
shape of the 3D printed inner shell of the fuselage).
3. Wing Loading
1
𝑥
a. 𝑆 = 3𝑖𝑛(17.5𝑖𝑛) + (2) (3 + 3 (1 − (17.5𝑖𝑛))) 𝑥; Where S is the planar surface area.
1
2
b. 𝐿 = 𝜌𝑉∞ 2 𝑆𝐶𝐿 ; This expression gives a distributed load for Lift over the wingspan.
c. 𝑤(𝑥) = 𝑀𝑟𝑐 ⟨𝑥⟩−2 + 𝑅𝑟𝑐 ⟨𝑥⟩−1 + 𝐿⟨𝑥⟩0 ; Where this is the expression for the singularity
function of the wing approximated as a beam. The carbon fiber rod is assumed fixed and
the moment it perceives at the root cord will be the maximum stress. These equations
need to be converted to Matlab script so that validation can be quickly provided with
minor adjustments.