OK, I asked my friend "CHAT-GPT" some questions for you:
I asked:
Can you explain to me relationship between the height of the centre of gravity and the track width of a tricycle with respect to the trike's ability to rollover in a tight turn?
CHAT-GPT replied:
The relationship between the height of the center of gravity and the track width of a tricycle is critical when considering the trike's ability to rollover in a tight turn. The center of gravity is the point where the weight of an object is evenly distributed in all directions, while the track width is the distance between the wheels on either side of the tricycle.
In general, the higher the center of gravity of a tricycle relative to its track width, the more likely the trike is to tip over in a tight turn. This is because when the tricycle is turning, the weight of the vehicle and its occupants is distributed to the outside of the turn, creating a centrifugal force that can cause the trike to tip over.
If the center of gravity is too high relative to the track width, the trike will be more prone to tipping over during tight turns. On the other hand, if the center of gravity is lower relative to the track width, the trike will be more stable in tight turns.
Therefore, it is essential to design tricycles with a low center of gravity and a wide track width to ensure that they are stable and safe during tight turns.
So I asked:
Is there a formula to calculate the likelihood of a rollover with given track widths and centre of gravity heights?
CHAT GPT replied:
Yes, there are formulas that can be used to calculate the likelihood of a rollover for a tricycle with given track widths and center of gravity heights. One such formula is the "static stability factor" (SSF) which is a ratio of the distance between the center of gravity and the outer wheels, divided by half the track width.
The SSF formula is given by:
SSF = (h / 2) / (w / 2)
Where:
- h is the height of the center of gravity above the ground
- w is the track width of the tricycle
The SSF value is a measure of the stability of the tricycle during cornering, with higher values indicating greater stability. The SSF value should ideally be greater than 1.0 for a stable tricycle.
However, it is important to note that SSF is only one of many factors that contribute to a tricycle's stability and rollover resistance. Other factors such as tire size, suspension design, and vehicle speed can also affect stability and the likelihood of rollover. It is therefore essential to consider all these factors together to ensure the safe design and operation of tricycles.
So I followed up with:
Are there other formulas that would be useful in planning the layout of a tricycle with respect to stability?
CHAT GPT replied:
Yes, there are other formulas that can be useful in planning the layout of a tricycle with respect to stability. Here are a few:
- Weight transfer: During a turn, weight is transferred from the inside wheels to the outside wheels. The amount of weight transfer can be calculated using the following formula:
WT = (h / L) * m * g * tan(Φ)
Where:
- h is the height of the centre of gravity above the ground
- L is the distance between the front and rear axles
- m is the mass of the tricycle
- g is the acceleration due to gravity
- Φ is the angle of the turn (in radians)
- This formula can be used to determine how much weight will be transferred during a turn, which can help to design the suspension and steering system to handle the extra load.
- Roll moment: The roll moment is the torque acting on the tricycle that tends to make it roll over during a turn. It can be calculated using the following formula:
RM = (h / L) * m * g * w * sin(Φ)
Where:
- h is the height of the centre of gravity above the ground
- L is the distance between the front and rear axles
- m is the mass of the tricycle
- g is the acceleration due to gravity
- w is the track width of the tricycle
- Φ is the angle of the turn (in radians)
- This formula can be used to determine the maximum safe speed for a given turn radius, track width, and center of gravity height.
- Lateral acceleration: The lateral acceleration is the acceleration of the tricycle perpendicular to its direction of motion during a turn. It can be calculated using the following formula:
LA = v^2 / (g * R)
Where:
- v is the speed of the tricycle
- g is the acceleration due to gravity
- R is the radius of the turn
- This formula can be used to determine the maximum safe speed for a given turn radius and lateral acceleration. It can also be used to design the suspension and steering system to handle the lateral forces during a turn.
These formulas, along with the static stability factor formula mentioned earlier, can be used together to design a stable and safe tricycle with appropriate weight distribution, suspension design, and steering system.
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BUT the SSF given made no sense to me because if you kept the CofG height the same and increased the track the values would very quickly go to below 1. So I challenged CHAT GPT with:
The SSF formula makes no sense
Chat GPT replied:
I apologize for the confusion. I made an error in the SSF formula in my previous response. Here is the corrected formula:
SSF = (h / 2) / (sqrt(w^2 + d^2) / 2)
Where:
- h is the height of the center of gravity above the ground
- w is the track width of the tricycle
- d is the wheelbase of the tricycle, which is the distance between the front and rear wheels
The SSF is a measure of the stability of the tricycle during cornering, with higher values indicating greater stability. The SSF value should ideally be greater than 1.0 for a stable tricycle.
Again, I apologize for any confusion caused by my previous response, and I hope this corrected formula helps clarify the relationship between the centre of gravity, track width, and wheelbase of a tricycle.
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So there you are Paul, this is the info you were looking for I think. I wish I understood it.
The SSF is probably the rudimentary one to start with.
Its the sort of thing a chap should make into a spreadsheet I think.