CG, TW, WB estimations - 9/2024

Owned by Kayla Lee
Last updated: Sep 16, 2024
5 min read

the damn preview isnt working… ill fix it later -

According to WSC book: determining CG TW and WB can be quite arbitrary. Finding the CG requires overall weight and wheelbase - these two things do not have an explicit method of calculation. They are typically just values estimated from pre-existing designs.

Goals:

  • estimate overall new weight

  • estimate CG

  • estimate weight distribution across front to rear axles

  • can get a rough est. of TW if the weight distribution w the assumed inputs are within our goal range of 60-70 front

  • after this - polar moment of inertia can be calculated

I have estimated the CG and weight distribution of our new vehicle according to:

Overview:

  1. WSC average values

    1. gave us a range of typical WB

    2. gave us examples of calculating CG distribution

  2. pre-existing daybreak weight values and dimensions - VDR

    1. battery weight - 30kg

    2. frame - ~187lbs

    3. 4.5 m length

    4. approx distance of significant masses from front axle

  3. system specific goals for the new car

    1. frame weight reduction

    2. occupant cell relocation

    3. 3 wheel assemblies

  4. regulations - give us a rough max and a min - regs

    1. battery - 30kg max

    2. max body length

    3. TW to WB ratio 1.5

my inputs:

MASSES (as reccomended to include by WSC):

  • Driver + ballast =

  • frame = 120lbs

    • daybreak = 828.74 lbs

    • goal to cut by 30% ~

    • also lines up with WSC approx. example

  • battery = 30kg

    • daybreak and should stay roughly the same

    • max by regs

  • “everything else” approx = 197 lbs

    • WSC

Overall weight estimation: 559.5lbs

This value seems to be an exageration and is much lower than Daybreak’s overall weight. If you account for the fact that we will have a 30% lighter frame ideally, an aeroshell that is ideally more narrow while keeping about the same top shell array surface area, and we will lose unsprung mass and rear suspension assembly weight: then 559.5 lbs is achievable/realistic to some extent.

Additionally (by WSC), lead acid battery stock class solar cars are about 850 lbs and lithium-polymer battery open class cars are around 600 lbs. - our lithium-ion batteries put us around the open class 600 lb range theoretically if we were to make all these adjustments.

5.0 m length body

2.2 m width body

1.6 m height

2.5 m WB

830 lb stock class weight

197 lb “everything else” weight @ center of the car

80 kg - 176 lb driver + ballast

336 lb batteries ( this is where their excess weight comes from)

 

Distances x from the front axle / nose:

 

image-20240917-034523.png

 

 

WSC gives us these distances x from the front axle of all their point masses: they also use the max length of the body 5m and it is alluded that they are modeling a 3-wheel vehicle due to the increased wheelbase and their rough positions of all significant weight factors are distributed with 60-70% of weight to front axle in mind.

Their driver and ballast CG is located .3m from the front axle, much closer than where we had it on DB. I use .3 m as well for ours.

Batteries for their car as well as ours is located behind the driver. For our model however, the batteries are the farthest from the front axle unlike theres where the batteries are right behind the driver. Based off of our occupant cell shape reconfigurations and the fact we may try to keep the overall shape of the back of the frame similar from DB: the batteries CG would most likely be located closer to the rear axle, behind the center of the car body where “everything else” CG is located to represent the shell and electronics. This is fine because it is the most realistic packaging that we have achieved already, and it less of an issue because ours are significantly lighter than the WSC example battery mass. I centered frame CG at the center of the WB. Regardless, it is similar to the WSC distributions.

 

To compare the WSC example dimensions to daybreak to achieve the new car design: Daybreak is 4.5m and ideally it does not need to actually get longer. Because the occupancy cell will likely be moved up, cutting the front of the frame that accounts for leg room, and the trailing wheel will need to be moved behind the DB frame; assuming that also the space frame will stay moderately the same in that the crumple zone in the front should stay the same distance: then the body (frame and aeroshell) moves forward in reference to the front axle. Assume the space between the back edge of frame to the end of aeroshell stays the same - as the nose is moving up but still need to account for array surface area requirements.

The average wheelbase according to WSC is 2-2.5m. WSC uses 2.5. Because the current wheelbase is 1.5m, and we need to theoretically move the rear axle to behind the DB frame to act as a trailing arm: the back wheel needs to move at least half the DB wheelbase to clear the frame so assume a 2.25m wheelbase for the purposes of this approximation.

 

image-20240917-035814.png

 

how i got the distances from front axle

driver + ballast - wsc and approx our preference

EE - body length / 2

Frame - wheelbase / 2

BB - checked validity by making sure at least .5 m was left from the WB (~edge of the frame in the back) and the end of BB to preserve the crash structure -

used the DB battery box dimensions = .67 m

2.25 (WB) - 1.425(BB CG from Fr. Ax.) = 0.825
0.825 (m between BB CG and Rr. Ax.) - 0.33 (1/2 BB length) = 0.495 m of frame to Rr. Ax.

leaving ab 1m of tail shell from the trailing arm wheel

Conclusion: see the scans

CG: 0.83 m behind front axle

Front: 62.75%

Rear: 37.25%

using the regs ratio of 1.5 > D2/D1 where D2 is WB and D1 is TW: D1 is at least 1.5m if WB is 2.25 m

 

 

 

 

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