did someone do a battery in a backpack awhile back?
since im here drinking tequila here is the query/result i got:
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Weight distribution and traction:
You’re right that placing the battery on the rider alone would increase the weight on the drive wheel, which can potentially increase traction. This is especially true if the front foot is lifted during launch, as you mentioned. -
Center of mass:
Placing the battery on the rider would raise the overall center of mass of the rider-vehicle system. This can have both positive and negative effects:
a. It could provide more leverage for the rider to apply force to the drive wheel.
b. However, it might also make the system less stable, especially during turns or at higher speeds. -
Lean angle and contact patch:
The higher center of mass would affect the lean angle required to maintain balance, especially during turns. This could potentially reduce the contact patch of the tire in some situations, which might counteract some of the traction gains. -
Rider comfort and control:
Having the battery on the rider might affect their comfort and ability to control the vehicle, especially if it’s a significant weight. -
Vehicle design considerations:
Placing the battery on the board allows for better integration with the vehicle’s systems and potentially better protection for the battery. -
Dynamic weight transfer:
During acceleration, weight naturally transfers to the rear wheel, which is usually the drive wheel. This happens regardless of battery placement, but the effect might be more pronounced with a rider-mounted battery.
In conclusion, while your statement about increased traction is theoretically correct in a static situation, the real-world implications are more complex. The overall performance, stability, and safety of the vehicle depend on a balance of these factors, which is why most electric skateboards and similar vehicles have the battery integrated into the board itself.
Dynamic Load Transfer:
During acceleration, there's a rearward weight shift due to inertia. This phenomenon, known as load transfer, is described by the equation:
ΔWr = (m * a * h) / L
Where:
ΔWr = change in rear axle load
m = total mass
a = acceleration
h = height of center of gravity (CG)
L = wheelbase
With the battery on the rider, ‘h’ increases, potentially amplifying this effect.
Rotational Inertia:
The moment of inertia (I) of the system changes with battery placement. For a rider, we can approximate using the parallel axis theorem:
I = Icm + md²
Where Icm is the moment of inertia about the center of mass, m is the mass, and d is the distance from the axis of rotation. This affects the system’s resistance to angular acceleration.
Tire Deformation and Contact Patch:
Tire behavior follows the Pacejka "Magic Formula":
Fy = D * sin(C * arctan(B * α - E * (B * α - arctan(B * α))))
Where Fy is the lateral force, and α is the slip angle. Coefficients B, C, D, and E depend on tire properties and normal force, which changes with weight distribution.
Gyroscopic Effects:
The precession torque (τ) on a spinning wheel is given by:
τ = I * ω * Ω
Where I is the wheel’s moment of inertia, ω is its angular velocity, and Ω is the angular velocity of the lean. This effect becomes more pronounced at higher speeds and can influence stability.
Control Theory Perspective:
The system can be modeled as an inverted pendulum, with the state-space representation:
[θ’‘] = [0 1][θ] + [0][u]
[θ’ ] = [g/l 0][θ’] + [1/ml²]
Where θ is the angle from vertical, l is the pendulum length, and u is the input torque. Battery placement affects ‘l’ and ‘m’, changing the system’s natural frequency and damping ratio.
Aerodynamics:
The drag force is given by:
Fd = (1/2) * ρ * v² * Cd * A
Where ρ is air density, v is velocity, Cd is the drag coefficient, and A is the frontal area. Battery placement affects the rider’s posture and thus A and Cd.
Material Stress:
If the battery were integrated into a wearable harness, we'd need to consider the stress (σ) on the harness material:
σ = F / A
Where F is the force applied and A is the cross-sectional area of the material.
Electrical Considerations:
Wire length from battery to motor would increase, leading to greater resistance (R) and power loss (P):
P = I²R
Where I is current and R is resistance.
Thermodynamics:
Heat dissipation from the battery becomes more critical when worn by the rider. The heat transfer rate (Q) is given by:
Q = h * A * ΔT
Where h is the heat transfer coefficient, A is the surface area, and ΔT is the temperature difference.
i think the board will likely be more tame with the battery directly attached
