What is Center of Gravity?
Every mass has a single point at which its entire weight effectively acts. Understanding it starts with breaking the system into parts.
The center of gravity (CoG) is the weighted average position of all mass in a system — expressed as a coordinate in space. For a bicycle and rider, the system is complex: frame, wheels, components, body segments, gear, helmet, pack. Every piece has a mass and a position.
BikeSPEZL breaks this into a layered model: first calculate the bike alone (B_COG), then the rider alone (R_COG), then combine them into the full-system T_COG. When the bike starts moving, T_COG becomes D_COG — a dynamic quantity that carries momentum from acceleration and braking.
B_COG — Bike Center of Gravity
Start with the bike alone. Every part has a mass and a 3D position relative to the BB.
B_COG is calculated from all individual bike components: frame, fork, wheels, shock, handlebar, stem, cranks, saddle, seatpost, brakes, drivetrain — every part you've catalogued. Each part contributes a mass point at its approximate position relative to the bottom bracket (BB = origin 0, 0, 0).
B_COG = Σ(mᵢ · pᵢ) / Σmᵢmᵢ = mass of part i · pᵢ = 3D position relative to BB
The biggest contributors to B_COG position are typically the frame (largest single mass), wheels (spread fore/aft and low), and battery + motor on e-bikes (heavy, often centrally located). Swapping a component — say from alloy to carbon wheels — will shift B_COG measurably.
- 1Heavier rear wheel → B_COG shifts rearward
- 2Heavier shock/linkage → B_COG shifts rearward and slightly lower
- 3Longer fork → raises B_COG height (higher front axle)
- 4Carbon frame vs alloy → lighter overall, less effect on position
R_COG — Rider Center of Gravity
The rider is the dominant mass in the system — typically 60–70% of total weight. Every body segment and piece of gear counts.
R_COG combines all body segments from the BDC (Body Dimension Capture) scan — feet, shins, femurs, pelvis, torso, arms, head — plus the gear set: helmet, protectors, shoes, pack, clothing. Each segment has a known mass and a 3D position that depends on the rider's position on the bike.
R_COG = Σ(mⱼ · pⱼ) / Σmⱼmⱼ = mass of body segment or gear item j · pⱼ = 3D position at current riding position
Because the rider position changes with bar height, saddle setback, and ergonomy preference, R_COG is geometry-dependent. Raising the bars shifts the torso more upright, moving R_COG upward and slightly rearward. Lowering the saddle changes hip position and shifts R_COG downward.
T_COG — True Center of Gravity
Combine B_COG and R_COG to get the full-system CoG at rest. This is the baseline for everything that follows.
T_COG is simply the mass-weighted average of B_COG and R_COG. Because the rider outweighs the bike, T_COG always lies closer to R_COG than to B_COG. It's the reference position for comparing setups: how does raising the bars move T_COG? How does a heavier pack affect it?
T_COG = (M_b · B_COG + M_r · R_COG) / (M_b + M_r)M_b = total bike mass · M_r = total rider+gear mass
T_COG is computed at the static sag position — suspension compressed to the rider's set sag percentage. This is the real-world at-rest state, not the unloaded geometry. A change in sag affects axle heights, which affects BB position, which affects where the rider sits, which moves both R_COG and T_COG.
- 1Higher bars → T_COG moves up and slightly back
- 2More rear sag → BB drops, rider drops, T_COG drops
- 3Heavier pack mounted high → T_COG rises noticeably
- 4Shorter stem → rider sits more upright, T_COG rises and shifts back
D_COG — Dynamic Center of Gravity
Once the bike moves, T_COG becomes D_COG — it now carries inertia from acceleration and braking. This is where ride dynamics begin.
D_COG is T_COG in motion. The key difference: D_COG carries momentum. Under braking, the system's inertia loads the front wheel and unloads the rear — mass effectively shifts forward. Under acceleration, inertia shifts mass rearward, loading the rear wheel.
The magnitude of the D_COG shift depends on:
- 1T_COG height — higher CoG = more weight transfer per g of acceleration
- 2Wheelbase — shorter wheelbase = more sensitive to weight transfer
- 3Deceleration rate — harder braking = more forward load shift
- 4Acceleration rate — harder pedalling out of corners = more rear load shift
In BikeSPEZL's Ride Dynamics (R&D) module, D_COG is visualised in real time as you adjust suspension sag, rider position, and acceleration/braking inputs. The simulation shows exactly how load distributes across both wheels at any point in the ride.
Anti-Rise & Anti-Squat
Anti-Rise and Anti-Squat are the kinematic response of the suspension to D_COG forces — they can only be meaningfully optimised once D_COG is understood.
When you accelerate hard, the rear suspension wants to extend (squat) under the load shift. When you brake hard, the front fork wants to compress (dive) and the rear shock extends (rise). The bike's linkage geometry and D_COG position together determine how much of these forces are counteracted by the suspension kinematics.
- 1Anti-Squat — how much the rear suspension resists compression under power. 100% = neutral; >100% = extends under power; <100% = compresses.
- 2Anti-Rise — how much the rear suspension resists extension under braking. Affected by brake torque line through the pivot.
- 3Both values are calculated from the instantaneous force lines through the suspension linkage, relative to D_COG position.
- 4Changing T_COG height (by adjusting rider position or CoG of bike) directly changes the calculated Anti-Rise and Anti-Squat percentages.