Mass distribution, center of gravity and longitudinal load-transfer engineering on an e-scooter: static F_z,f / F_z,r, dynamic ΔN = m·a·h/L, wheelie / stoppie thresholds, anti-squat / anti-dive geometry and optimal brake bias

In the articles «Smooth acceleration and throttle control», «Braking technique», «Brake system engineering» §3, and «ABS engineering» §3, weight-transfer appears in three contexts: as rider technique (lower CG, lean forward before launch), as an ABS controller calibration parameter (front-wheel normal force determines peak μ·F_z), and as the entry point for brake-bias engineering (why the front caliper is 4-piston and the rear is 2-piston). None of these three describes mass distribution itself as a design discipline: where the designer puts the battery, how this affects a / b / h, why a 1000 mm wheelbase with 1.2 m CG has higher load-transfer sensitivity than a 1400 mm wheelbase with 0.7 m CG, how to choose optimal brake bias under real geometry.

This deep-dive is the eleventh engineering-axis after helmet, battery, brake-system, motor/controller, suspension, tire, lighting, frame/fork, speed-wobble, ABS — adding the longitudinal-and-vertical integrator-axis: static F_z,f and F_z,r at rest are the input data for EVERYTHING that happens afterwards. If CG shifts 50 mm rearward — that changes everything: stopping distance, wheelie threshold on launch, tire wear pattern, suspension sag, frame torque profile.

Prerequisite — understanding brake system physics (Pascal’s law, calipers) and longitudinal dynamics of the tire-road interface (peak μ-λ curve, friction circle).

1. Newton’s framework for rigid-body longitudinal dynamics

Treat scooter + rider as a single rigid body of total mass m (typically 90-110 kg — 70-90 kg rider + 15-30 kg scooter). Coordinate system — ISO 8855:2011 «Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary»:

Axis	Direction	Sign
x	Longitudinal, in the direction of travel	+ forward
y	Lateral, perpendicular to travel	+ leftward
z	Vertical, from ground upward	+ up

Geometric parameters (Cossalter §6.1, Foale §2.3):

Parameter	Symbol	Typical e-scooter value
Wheelbase	L	1000-1150 mm
Distance from front axle to CG	a	550-700 mm
Distance from rear axle to CG	b = L − a	350-500 mm
CG height above the road	h	1100-1300 mm (with rider)
Wheel radius	R	100-130 mm (8-10″)
h / L ratio	—	1.0-1.3

Comparison: motorcycles have L = 1300-1500 mm, h = 600-750 mm (lower, because the rider sits), so h/L = 0.4-0.55 — 2-3× lower than e-scooters. Bicycles: L = 1000-1200 mm, h = 1000-1100 mm, h/L = 0.9-1.0 — close to e-scooter, but the rider constantly changes posture. Key insight: the e-scooter is the most vulnerable road two-wheeler category by longitudinal dynamics.

Newton’s second law for translation and rotation:

$$\sum F_x = m \cdot a_x$$ $$\sum F_z = m \cdot a_z = 0 \text{ (during steady motion on a level surface)}$$ $$\sum M_{CG} = I_{yy} \cdot \alpha_y \text{ (pitch rate)}$$

where I_yy is the pitch moment of inertia about the lateral axis through the CG, typically 8-15 kg·m² for a scooter with rider.

For steady-state (constant a_x, no pitch oscillation): α_y = 0, so ΣM_CG = 0 — the sum of moments from normal forces, brake forces, and the longitudinal inertial “effective” moment = 0. This yields the load-transfer formula (section 3).

Free-body diagram for a single-track two-wheeler:

                    ┌──── m·g ────┐ (gravity, through CG)
                    │             │
            ┌───────●─────────────●──────┐  ← CG at height h
            │                            │
            │←─── a ────→│←──── b ──────→│
            │                            │
        F_x,f                        F_x,r  ← longitudinal tire forces
        F_z,f                        F_z,r  ← normal tire forces
            ▼                            ▼
        ════●════════════════════════════●════  ← ground
         front wheel                  rear wheel

where F_x,f, F_x,r are longitudinal forces at the wheels (negative under braking, positive under drive); F_z,f, F_z,r are normal (vertical) forces.

2. Static load distribution — F_z,f and F_z,r at rest

At rest (a_x = 0), summing moments about the rear contact patch:

$$F_{z,f} \cdot L - m \cdot g \cdot b = 0$$ $$F_{z,f} = \frac{m \cdot g \cdot b}{L}$$

Summing moments about the front contact patch:

$$F_{z,r} = \frac{m \cdot g \cdot a}{L}$$

Sanity check: F_z,f + F_z,r = m·g·(b + a)/L = m·g — the sum of normal forces equals weight. ✓

Worked example — a typical commuter e-scooter, Ninebot Max G30 + 75 kg rider:

• m = 19 kg (scooter) + 75 kg (rider) = 94 kg
• L = 1170 mm = 1.17 m
• a ≈ 660 mm = 0.66 m (CG shifted forward of geometric mid-wheelbase by tall handlebar)
• b = L − a = 510 mm = 0.51 m
• h ≈ 1180 mm = 1.18 m (with rider)
• m·g = 94 × 9.81 = 922.1 N

Static normal forces:

• F_z,f = m·g·b/L = 922.1 × 0.51 / 1.17 = 401.9 N (43.6 %)
• F_z,r = m·g·a/L = 922.1 × 0.66 / 1.17 = 520.2 N (56.4 %)

Typical e-scooter static distribution range: 35-45 % front / 55-65 % rear. Why rear-biased? CG is shifted rearward through rider posture (feet on the middle of the deck, hands forward on the bar, but the upper third of the mass — torso + head — sits above the CG, not displaced forward). If a = b = L/2, the distribution would be 50/50. Some hyperscooter models (Dualtron Storm, NAMI Burn-E 2) with dual-battery deck push CG further back → 25-35 % front / 65-75 % rear.

Comparison with other vehicle categories (Wong «Theory of Ground Vehicles» §3.1):

Vehicle	Front	Rear	Why
Sport motorcycle	45-50 %	50-55 %	Engine + fuel ahead of rear axle
Touring motorcycle	50-55 %	45-50 %	Balanced for long-haul comfort
Standard bicycle (rider hands on bar)	40-45 %	55-60 %	Analogous to e-scooter
TT bicycle (aero tuck)	50-55 %	45-50 %	Rider stretched low forward
Front-wheel-drive car	55-65 %	35-45 %	Powertrain forward
RWD performance car	48-52 %	48-52 %	Desired balance for cornering

E-scooter rear-biased static distribution has two consequences: (a) rear tire wear outpaces front 2-3× (confirmed by Lime fleet field data, 2022); (b) wheelie threshold is high (because the CG is closer to the rear axle — smaller moment-arm b).

3. Acceleration load transfer — ΔN = m·a·h/L

Under longitudinal acceleration a_x > 0 (forward), summing moments about the rear contact patch:

$$F_{z,f} \cdot L - m \cdot g \cdot b + m \cdot a_x \cdot h = 0$$

The third term is the inertial moment: mass m is accelerated by a_x (Newton’s second), and that “effective force” m·a_x acts at the CG at height h above the ground. Solving:

$$F_{z,f}(a_x) = \frac{m \cdot g \cdot b - m \cdot a_x \cdot h}{L} = F_{z,f}^{static} - \frac{m \cdot a_x \cdot h}{L}$$

$$F_{z,r}(a_x) = F_{z,r}^{static} + \frac{m \cdot a_x \cdot h}{L}$$

This is the fundamental load-transfer equation (Gillespie §3.3, Cossalter §6.2):

$$\boxed{\Delta N = \frac{m \cdot a_x \cdot h}{L}}$$

— the magnitude by which the front axle unloads and the rear axle loads up, directly proportional to acceleration a_x and the h/L ratio.

Worked example — the same Ninebot Max G30 + 75 kg rider, acceleration a_x = 0.3g = 2.94 m/s² (typical sport-mode launch):

• ΔN = m·a·h/L = 94 × 2.94 × 1.18 / 1.17 = 278.5 N
• F_z,f(0.3g) = 401.9 − 278.5 = 123.4 N (13.4 % of total weight)
• F_z,r(0.3g) = 520.2 + 278.5 = 798.7 N (86.6 %)

At 0.3g (a moderate acceleration) the front wheel falls from 43.6 % static load down to 13.4 % — a 3× drop! This means: in a corner with front-wheel side-slip the risk rises, on a bump the front fork has near-zero preload, the front tire loses grip.

h/L sensitivity comparison at the same a_x = 0.3g:

Vehicle	h (m)	L (m)	h/L	ΔN / m·g
Sport motorcycle	0.70	1.40	0.50	15.0 %
Touring motorcycle	0.75	1.50	0.50	15.0 %
Bicycle (commuter)	1.05	1.10	0.95	28.6 %
E-scooter (typical)	1.18	1.17	1.01	30.2 %
E-scooter (hyperscooter dual-battery)	1.25	1.17	1.07	32.0 %

E-scooter ΔN / m·g = 30.2 % means: at 0.3g acceleration, nearly a third of the weight migrates to the rear axle. At 0.5g — half. At 0.7g — 70 % is on the rear wheel and the front axle is unloaded to zero. This is the basis of the wheelie threshold (section 5).

Why high h/L for an e-scooter is a design constraint, not a bug:

• h is high because the rider stands (head + shoulder CG at ~1.5-1.7 m, balanced through feet on a ~0.1 m deck), and lowering the CG further is impossible without changing posture (crouching brings back the wobble window — see speed-wobble).
• L is short because portability is the product: a folded scooter into a car trunk or under a desk needs at most 1.2 m length. Extending to 1.5 m loses the fundamental market positioning.
• Conclusion: e-scooter h/L ≈ 1.0 is an inherent design constraint, not a fault. The designer compensates through other parameters (CG forward, suspension geometry, brake bias).

4. Braking load transfer — opposite sign

Under braking a_x < 0 (deceleration; convention Gillespie §4.2: a_x = -|deceleration|). Substituting into the load-transfer equation:

$$F_{z,f}(a_x) = F_{z,f}^{static} + \frac{m \cdot |a_x| \cdot h}{L}$$ $$F_{z,r}(a_x) = F_{z,r}^{static} - \frac{m \cdot |a_x| \cdot h}{L}$$

The front axle is loaded up, the rear unloads — opposite to acceleration.

Worked example — the same Ninebot Max G30 + 75 kg rider, deceleration |a_x| = 0.6g = 5.89 m/s² (intense emergency braking, the dry-asphalt μ limit for pneumatic tires):

• ΔN = m·|a|·h/L = 94 × 5.89 × 1.18 / 1.17 = 558.2 N
• F_z,f(0.6g) = 401.9 + 558.2 = 960.1 N (104 % of total weight)
• F_z,r(0.6g) = 520.2 − 558.2 = −38.0 N

F_z,r < 0 means the rear wheel lifts off the ground — this is the stoppie / forward pitchover threshold (detailed in section 6). At 0.6g emergency brake, an e-scooter is very close to stoppie. On a motorcycle with h/L = 0.5, the same 0.6g gives ΔN/m·g = 30 %, i.e. the rear tire still holds 55 % − 30 % = 25 % of weight — there is a safety margin. The e-scooter margin is near zero.

Implications for brake bias (detailed in section 9):

• At low-deceleration cruise braking (0.1-0.2g): rear-bias is optimal (because F_z,r > F_z,f at cruise).
• At emergency braking (0.5g+): almost all force is borne by the front wheel. Tip 80/20 → 90/10 front/rear distribution. This is why performance e-scooters have a 4-piston front caliper + 200 mm rotor + 2-piston rear caliper + 160 mm rotor (asymmetric capacity).
• If the rear brake locks at low F_z,r: the rear wheel skids, destabilising the vehicle — hence cycling/motorcycle teaching “front brake does 70 % of stopping” (Cossalter §8.4).

Tire μ envelope (Pacejka §1.3, peak μ for pneumatic on dry asphalt ≈ 0.9-1.0):

| Surface | μ_peak | Max sustainable |a_x| | |—|—|—| | Dry asphalt | 0.9-1.0 | 0.9g (88 %, tire-limited) | | Wet asphalt | 0.5-0.7 | 0.6g (60 %, tire-limited) | | Snow / ice | 0.1-0.3 | 0.15g (15 %) | | Sand / gravel | 0.3-0.5 | 0.4g (40 %) |

On wet asphalt μ_peak ≈ 0.6 — emergency braking is capped at 0.6g even with a perfect tire. On a load-transfer-limited e-scooter, this again means the stoppie threshold dominates (because g·a/h ≈ 0.55g — below the tire limit; the constraint is structural, not rubber stickiness).

5. Wheelie threshold — limiting a_x for front wheel lift-off

Wheelie condition: F_z,f = 0 (front wheel loses contact with the road).

From the load-transfer equation:

$$F_{z,f}^{static} = \frac{m \cdot a_{wheelie} \cdot h}{L}$$ $$\frac{m \cdot g \cdot b}{L} = \frac{m \cdot a_{wheelie} \cdot h}{L}$$

$$\boxed{a_{wheelie} = g \cdot \frac{b}{h}}$$

This is the fundamental wheelie threshold — a function only of the b/h ratio (Cossalter §6.6, Foale §3.5).

Worked example — Ninebot Max G30 + 75 kg rider: a_wheelie = 9.81 × 0.51 / 1.18 = 4.24 m/s² ≈ 0.43g.

This scooter is wheelie-limited at 0.43g, i.e. 4.24 m/s² — exceed that acceleration and the front wheel lifts off. If the controller does not limit peak motor power, on launch with 100 % throttle the front wheel goes up the moment 0.43g is exceeded.

Reference table — wheelie thresholds across e-scooter classes:

Class	b (m)	h (m)	a_wheelie / g	Comment
Lightweight commuter (Xiaomi 1S)	0.55	1.15	0.48	High threshold, few performance motors reach it
Standard commuter (Ninebot Max G30)	0.51	1.18	0.43	Borderline on sport-mode launch
Performance (Apollo Phantom)	0.48	1.22	0.39	Regularly reached on launch without soft-start
Hyperscooter (Dualtron Storm)	0.45	1.25	0.36	Wheelie at 100 % throttle is guaranteed
Off-road (NAMI Burn-E 2)	0.55	1.28	0.42	Larger b thanks to CG forward

Modern performance models with peak motor power of 3-6 kW easily exceed 0.5g launch acceleration → wheelie threshold is reached in the first 0.3-0.5 s of throttle response. This is why a soft-start ramp (controller-side peak-current limiting for the first 0.5-1.0 s) is standard for performance models: it keeps a_x < a_wheelie on launch (detailed in «Smooth acceleration»).

Wheelie threshold on a gradient. If travelling on a gradient θ (uphill), gravity contributes to the longitudinal force balance. Wheelie condition (sum of moments at the rear-wheel contact patch = 0):

$$m \cdot a_x \cdot h \cos\theta + m \cdot g \cdot h \sin\theta = m \cdot g \cdot b \cos\theta$$

Solving for a_x:

$$\boxed{a_{wheelie}(\theta) = g \cdot \left(\frac{b}{h} - \tan\theta\right) \cos\theta \approx g \cdot \frac{b}{h} - g \cdot \sin\theta}$$

(approximation valid for small θ). On a 10 % gradient (θ ≈ 5.71°, sin θ ≈ 0.1):

a_wheelie(10 %) ≈ 0.43g − 0.1g = 0.33g

On a 20 % gradient: a_wheelie ≈ 0.23g. On a 30 % uphill: a_wheelie ≈ 0.13g — virtually any throttle triggers a wheelie. This is why uphill launch on a performance e-scooter mandates body-forward technique + ECO mode (detailed protocol in the acceleration article).

Reactive motor torque adds another wheelie component, not captured by the simple a_wheelie = g·b/h. A hub motor in the rear wheel applies forward torque to the wheel; by Newton’s third law the stator pushes back on the housing with equal and opposite torque — and through it on the frame. This reaction torque raises the scooter’s nose independently of longitudinal acceleration. Limebeer & Sharp 2006 §3 quantifies this contribution as τ_reaction = T_motor / r_wheel — for a motor torque of 50 N·m at a 0.1 m radius, that is 500 N of effective vertical “lifting force” through the rear axle. On an e-scooter with a short wheelbase, this contribution is half of the total wheelie moment at peak motor torque. Modern motorcycles with longer wheelbases are less sensitive.

6. Stoppie / forward pitchover threshold — limiting |a_x| for rear-wheel lift-off

Stoppie condition: F_z,r = 0 (rear wheel loses contact with the road while braking).

By analogy with the wheelie:

$$\boxed{|a_{stoppie}| = g \cdot \frac{a}{h}}$$

where a is the distance from CG to the front axle.

Worked example — the same Ninebot Max G30 + 75 kg rider: |a_stoppie| = 9.81 × 0.66 / 1.18 = 5.49 m/s² ≈ 0.56g.

This scooter has a stoppie threshold of 0.56g. That is, emergency braking with deceleration > 0.56g (5.49 m/s²) → the rear wheel lifts off → forward pitchover (rider tumbles over the front wheel).

Reference table — stoppie thresholds:

| Class | a (m) | h (m) | |a_stoppie| / g | |—|—|—|—| | Lightweight commuter (Xiaomi 1S) | 0.60 | 1.15 | 0.52 | | Standard commuter (Ninebot Max G30) | 0.66 | 1.18 | 0.56 | | Performance (Apollo Phantom) | 0.67 | 1.22 | 0.55 | | Hyperscooter (Dualtron Storm) | 0.70 | 1.25 | 0.56 | | Off-road (NAMI Burn-E 2) | 0.60 | 1.28 | 0.47 |

E-scooter |a_stoppie| ≈ 0.5-0.6g — compared to the tire-limited dry-asphalt max of 0.9g, this means pitchover, not tire slip, is the first failure mode under emergency braking. This is fundamentally different from a motorcycle (where |a_stoppie| ≈ 1.3g at a/h ≈ 1.3, and tire is always the limit) and a car (which reaches the tire limit long before any wheelie — |a_stoppie| ≈ 1.5-2.0g).

Design consequence: an e-scooter brake system cannot exploit the full tire-friction potential — it is pitchover-limited. This is why ABS on an e-scooter (engineering article) is not an “escape from lockup” like on a car, but rather — maintenance of |a_x| in the tire-peak window AND below pitchover. Bosch eBike ABS is calibrated for a target |a_x| ≈ 0.4-0.5g (protecting against pitchover).

Forward pitchover on a gradient (downhill): on a descent θ < 0 (downhill), the gravity component aids the decelerator (component along −x). The stoppie threshold shrinks accordingly:

$$|a_{stoppie}(\theta_{downhill})| ≈ g \cdot \frac{a}{h} - g \cdot |\sin\theta|$$

On a 10 % downhill: |a_stoppie| ≈ 0.56g − 0.1g = 0.46g. On a 20 % downhill: ≈ 0.36g. This is why descending hills + emergency braking is the top stoppie-incident factor (CPSC e-scooter injury data 2024 shows 18 % “front-pitchover” mechanism in downhill incidents).

7. Cornering lateral load transfer — brief cross-link

Lateral load transfer in a corner is a separate axis (y-direction), detailed in «Cornering and lean technique» and «Suspension engineering» §5. The canonical formula (Pacejka §1.6):

$$\Delta N_{lateral} = \frac{m \cdot v^2 / r \cdot h}{T}$$

where T is track width (for a single-track vehicle like an e-scooter, T = 0 → lateral load transfer is expressed through lean angle θ_lean = arctan(v²/(r·g)) instead of direct ΔN, and mass is transferred VERTICALLY through the CG to the tire contact patch). This is why a single-track vehicle leans into the corner rather than tilting via outboard transfer.

Combined load transfer (longitudinal + lateral together — entering a corner under braking, exiting under acceleration) is the friction circle problem (Pacejka §3.2). The tire μ envelope bounds the sum:

$$\sqrt{F_x^2 + F_y^2} \leq \mu \cdot F_z$$

This is why emergency braking inside a corner is fundamentally ineffective on an e-scooter: longitudinal load transfer unloads the front wheel, lateral load demands grip of the same wheel, the vector sum exceeds μ·F_z → tire slip → crash. Canonical advice: straighten the vehicle first, then brake (MSF Basic RiderCourse, Cossalter §8.6).

8. Anti-squat and anti-dive suspension geometry

Anti-squat is the fraction of acceleration load transfer compensated by (rear) suspension geometry rather than by spring/damper compression. At 100 % anti-squat: under acceleration the rear suspension does not compress at all (geometry redirects ALL of the load transfer through the swingarm pivot). At 0 % anti-squat: the spring system absorbs 100 % of ΔN.

Anti-squat formula for a standard motorcycle / single-pivot rear swingarm (Foale §4.4):

$$\text{anti-squat} % = \frac{\tan\beta}{\tan\gamma} \times 100 %$$

where:

• β — angle from the rear contact patch up to the swingarm pivot
• γ — angle from the rear contact patch up to the CG

E-scooter case: most e-scooters have a rigid rear axle (no swingarm) → β = 0 → anti-squat = 0 %. All of ΔN under acceleration compresses the rear suspension (if one exists — at the bottom-out limit), or simply tire deflection (if no suspension is fitted → tire pressure rises, ride harshens).

Some hyperscooter models do have swingarm rear suspension (Dualtron X2, NAMI Burn-E 2 with dual-pivot linkage) — their anti-squat is ≈ 30-50 %, partially isolating the rider from rear-tire squat and preventing bottom-out under full-throttle launch.

Anti-dive is the fraction of braking load transfer compensated by front-fork geometry. For a telescopic fork (with original straight-axis travel), anti-dive ≈ 0 % — the fork compresses fully under load transfer, additionally reducing trail and producing “pitch-dive feel”. This is an inherent telescopic-fork limitation and why motorcycle racing has moved since the 1990s towards alternative front-suspension geometries (Telelever on BMW, Hossack/Fior linkage on Bimota Tesi).

E-scooter front suspension: most models have rigid fork (no front suspension) or basic spring/hydraulic telescopic (Ninebot Max G30, NAMI Burn-E 2 with 70-90 mm travel). Anti-dive = 0 for telescopic = ΔN compresses the fork fully. At 0.5g emergency braking with 470 N of extra front ΔN, the fork compresses 60-80 % of its travel — approaching bottom-out. That is why brake-induced pitch-dive (~3-5° forward rotation) is the typical feel of an e-scooter emergency brake, and why suspension geometry additionally degrades (trail shrinks → wobble probability rises — see speed-wobble).

9. Optimal brake force distribution — ratio F_brake,f / F_brake,r

Ideal brake bias is the share of total braking force delivered to the front vs the rear so that both wheels reach peak μ SIMULTANEOUSLY at a given |a_x| (Gillespie §4.4, Cossalter §8.4). If bias is weighted incorrectly, one wheel locks earlier (wasting friction potential).

For steady-state braking with μ = μ_f = μ_r (same tires front and rear) and load transfer accounted for:

$$\frac{F_{brake,f}}{F_{brake,r}} = \frac{F_{z,f}(a_x)}{F_{z,r}(a_x)} = \frac{F_{z,f}^{static} + m \cdot |a_x| \cdot h / L}{F_{z,r}^{static} - m \cdot |a_x| \cdot h / L}$$

Worked example — Ninebot Max G30 + 75 kg rider on dry asphalt at |a_x| = 0.5g:

• F_z,f(0.5g) = 401.9 + 94 × 4.91 × 1.18 / 1.17 = 401.9 + 465.1 = 867.0 N (94 % of weight)
• F_z,r(0.5g) = 520.2 − 465.1 = 55.1 N (6 % of weight)
• Ideal front/rear ratio: 867.0 / 55.1 ≈ 15.7 / 1 → 94 % front, 6 % rear

At low-deceleration cruise braking |a_x| = 0.1g:

• F_z,f(0.1g) = 401.9 + 93.0 = 494.9 N (54 %)
• F_z,r(0.1g) = 520.2 − 93.0 = 427.2 N (46 %)
• Ratio: 494.9 / 427.2 ≈ 1.16 / 1 → 54 % front, 46 % rear

Brake bias is non-linear: the higher |a_x|, the more strongly bias is pulled forward. That means fixed mechanical bias (i.e. identical diameters/calipers front and rear) is completely wrong. Modern e-scooters get this right via asymmetric capacity:

Segment	Front calipers	Rear calipers	Implied bias
Lightweight	1-piston / 140 mm rotor	None / drum / electronic regen only	~95/5 (rear-only emergency)
Standard commuter	2-piston / 160 mm	1-piston / 140 mm	~70/30
Performance	4-piston / 200 mm	2-piston / 160 mm	~75/25
Hyperscooter (Dualtron X2, NAMI BE2)	4-piston / 200 mm Magura/Zoom	4-piston / 180 mm	~70/30
ABS-equipped (Niu KQi 4 Pro)	2-piston / 180 mm + ABS	1-piston / 140 mm	~80/20 + dynamic ctrl

Why not 90/10 on a performance model? Because bias must remain valid at ALL decelerations, not just emergency stops. At low cruise braking, 90/10 bias overheats the front (rear is at low duty cycle) and produces wheelchair-style “diving feel” even on a gentle stop. Compromise: 70-80 % front bias + rider technique adjustment (more front-lever pressure on emergency, balanced on cruise).

ABS-equipped models (Niu KQi 4 Pro, NAMI Burn-E 2 ABS option) have dynamic bias via the modulator: ECU keeps F_brake,f at peak μ·F_z,f, regardless of rider input. This removes the fixed mechanical compromise.

10. Payload / cargo CG shift — how a backpack, basket, or passenger changes everything

Payload does not just add mass — it shifts CG. Total CG of the new system (rider + scooter + payload):

$$h_{eff} = \frac{m_r \cdot h_r + m_p \cdot h_p}{m_r + m_p}$$

where m_r, h_r are mass and CG of rider+scooter; m_p, h_p are mass and height of the payload centre.

Backpack on the rider’s back (typical 10-kg backpack):

• m_p = 10 kg, h_p ≈ 1.45 m (height of the backpack centre)
• m_r = 94 kg, h_r = 1.18 m
• h_eff = (94 × 1.18 + 10 × 1.45) / 104 = (110.9 + 14.5) / 104 = 1.206 m
• CG rose by 26 mm (from 1.18 to 1.206 m)

This changes h/L = 1.18 / 1.17 = 1.01 to h/L = 1.206 / 1.17 = 1.031 (+3.1 %). Wheelie threshold: a_wheelie = g·b/h = 9.81 × 0.51 / 1.206 = 4.15 m/s² ≈ 0.423g (vs no-backpack 0.43g, -2 %). Stoppie threshold: |a_stoppie| = 9.81 × 0.66 / 1.206 = 5.37 m/s² ≈ 0.55g (vs 0.56g, -1.8 %).

A 10-kg backpack is a small change. But a 20-kg backpack or a passenger (ideally NOT, since most e-scooters are spec’d for a single rider, e.g. EN 17128 §5.1):

• m_p = 65 kg (passenger), h_p ≈ 1.45 m (CG of a second person on the scooter)
• m_r = 94 kg, h_r = 1.18 m
• h_eff = (94 × 1.18 + 65 × 1.45) / 159 = (110.9 + 94.3) / 159 = 1.290 m
• CG rose by 110 mm (+9.3 %)

Wheelie threshold drops to 0.39g, stoppie to 0.50g. Combined with mass doubling (m_total = 159 kg → kinetic energy doubles, brake heat doubles, frame loading doubles — detailed in «Carrying cargo and payload»).

Cargo on the stem wall (handlebar bag, 5-10 kg) shifts CG forward (a decreases):

• 8 kg on the handlebar, a_bag ≈ 0.5 m (forward of the front axle by ~50 mm in front of the wheel):

This shifts CG forward, which raises the wheelie threshold (b grows) but lowers the stoppie threshold (a shrinks). On a performance scooter with a front cargo basket, emergency braking becomes more unstable — a rarely discussed design trade-off.

Rear cargo basket (typically 5-15 kg, common on delivery e-scooters Bird / Apollo Pro Cargo):

• 12 kg on the rear basket, h_basket ≈ 0.45 m, b_basket = b + 0.3 m (basket REAR of rear axle):
• CG shifts rearward AND lower. Wheelie threshold drops (gear closer to the rear axle), stoppie threshold rises.

11. Standards and test procedures

E-scooter / PLEV (Personal Light Electric Vehicle) regulations do not specify mass-distribution requirements in great detail — that is left to engineers, but test procedures are defined:

EN 17128:2020 «Personal light electric vehicles — Safety requirements and test methods»:

• §5.1: max rider weight 100 kg (the manufacturer may declare higher).
• §6.5: dynamic frame fatigue test 50 000 cycles with a 1.3 dynamic factor — implies design for worst-case m·g·1.3 loading.
• §7.6: curb-mount test — the vehicle must not tip over from a 20 mm vertical drop at total mass (m_rider + m_scooter) — implicit max h constraint.
• §6.4: frame impact test 22 kg × 180 mm drop — absorbing energy 38.8 J — implies the design target for the frame’s torsional moment of inertia.

ISO 8855:2011 «Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary» — canonical axis convention used in all engineering calculations longitudinal/lateral/vertical.

ECE R78 (UN ECE motorcycle Type Approval) — reference for two-wheeler vehicle dynamics, formally non-applicable to PLEV, but test procedures (braking distance, stability) are borrowed de facto in the industry.

ISO 4210-3:2014 (bicycle frame+fork tests) — adjacent reference for frame design under cyclic loading, frequently cited in e-scooter frame engineering.

How this affects design: a manufacturer targeting EN 17128:2020 compliance cannot simply declare m_rider = 100 kg — it must demonstrate stability margin on the test procedures under worst-case load distribution (typically front-heavy rider posture + 10-kg hanging cargo on the handlebar). Manufacturers in the hyperscooter segment (>$3000 MSRP) often exceed EN 17128 specs and declare m_rider = 120-150 kg (for passenger-or-cargo-tolerant use), which requires h/L adjustment via a lower deck or longer wheelbase.

Recap: 9 design-side takeaways

1. Newton + ISO 8855 framework: longitudinal dynamics is a rigid-body model with ΣF_x = m·a_x and ΣM_CG = I_yy·α_y; static load distribution with F_z,f = mg·b/L and F_z,r = mg·a/L, dynamic transfer with ΔN = m·a·h/L.

2. E-scooter h/L ≈ 1.0 — 2-3× higher than motorcycle (0.5) — means 2-3× higher load-transfer sensitivity. At 0.3g acceleration, 30 % of weight migrates; at 0.5g — half.

3. Static distribution 35-45 % front / 55-65 % rear via rear-biased rider posture. Hyperscooter with dual-battery deck is even more rear-biased (25-35 % front).

4. Wheelie threshold a_wheelie = g·b/h — for a typical e-scooter, 0.4-0.5g. Performance motors with peak power of 3-6 kW easily exceed it — soft-start ramp in the controller is critical. Uphill gradient reduces the threshold linearly (g·sin θ subtracts).

5. Stoppie threshold |a_stoppie| = g·a/h — for a typical e-scooter, 0.5-0.6g. This is lower than the tire-friction limit 0.9g on dry asphalt — pitchover, not slip, is the first failure mode of emergency braking. Downhill reduces the threshold (g·|sin θ| subtracts).

6. Anti-dive ≈ 0 % for a telescopic front fork — the fork compresses fully under load transfer, additionally reducing trail and producing brake-induced pitch-dive (3-5° forward rotation). Inherent telescopic-geometry limit.

7. Anti-squat ≈ 0 % for a rigid rear axle (most commuter models); 30-50 % for swingarm-rear hyperscooters — partially isolates the rider from rear squat on launch.

8. Optimal brake bias is non-linear — from 54/46 (cruise braking 0.1g) to 95/5 (emergency 0.5g+). Fixed mechanical bias (identical calipers) is wrong; the right approach is asymmetric capacity 4-piston front + 2-piston rear (performance), or ABS dynamic modulation (Niu KQi 4 Pro, NAMI Burn-E 2).

9. Payload shifts CG: backpack on the rider’s back +26 mm of h_eff (10 kg), passenger +110 mm (65 kg), forward cargo a−, rear cargo a+. Each shift changes wheelie/stoppie thresholds, brake bias, frame loading. EN 17128 max rider 100 kg is a hard design constraint.

Adjacent topics

• Brake system engineering — hydraulics, calipers, DOT fluids, friction materials.
• ABS engineering — closed-loop control that keeps F_brake,f = μ·F_z,f at peak.
• Smooth acceleration and throttle control — rider technique for launch with weight-transfer control.
• Braking technique — rider technique for emergency braking without stoppie.
• Frame and fork engineering — the structural axis that integrates all longitudinal forces.
• Suspension engineering — anti-dive / anti-squat geometry in detail.
• Climbing hills and gradeability — uphill launch and modified wheelie thresholds.
• Descending hills and brake thermal management — downhill emergency braking and stoppie risk.
• Carrying cargo and payload — payload CG shift in detail.
• Speed wobble and weave stability — how brake-induced pitch-dive reduces trail and triggers wobble.

Sources

Canonical engineering handbooks:

• Gillespie T.D. «Fundamentals of Vehicle Dynamics» SAE International 1992, ISBN 978-1-56091-199-9 — §1.5 axle loads, §3 acceleration performance, §4 braking performance (canonical reference for the entire discipline).
• Cossalter V. «Motorcycle Dynamics» 2nd ed. 2006, ISBN 978-1-4303-0861-4 — §6 longitudinal dynamics, §8 braking.
• Foale T. «Motorcycle Handling and Chassis Design: The Art and Science» 2nd ed. 2006, Tony Foale Designs, ISBN 978-84-933286-3-4 — §2.3 geometry, §3.5 wheelie and §4.4 anti-squat / anti-dive.
• Pacejka H.B. «Tire and Vehicle Dynamics» 3rd ed. 2012, Butterworth-Heinemann / Elsevier, ISBN 978-0-08-097016-5 — §1.3 longitudinal slip, §1.6 lateral dynamics, §3.2 friction circle.
• Wong J.Y. «Theory of Ground Vehicles» 4th ed. 2008, Wiley, ISBN 978-0-470-17038-0 — §3.1 weight distribution, §3.2 braking performance.
• Genta G., Morello L. «The Automotive Chassis: Volume 1 — Components Design» 2nd ed. 2020, Springer Mechanical Engineering Series, ISBN 978-3-030-35634-0.

Academic papers:

• Limebeer D.J.N., Sharp R.S. «Bicycles, motorcycles, and models» IEEE Control Systems Magazine 26(5):34-61 (2006), DOI 10.1109/MCS.2006.1700044 — reaction torque contribution to the wheelie moment.
• Meijaard J.P., Papadopoulos J.M., Ruina A., Schwab A.L. «Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review» Proc. R. Soc. A 463:1955-1982 (2007), DOI 10.1098/rspa.2007.1857.
• Sharp R.S. «The stability and control of motorcycles» Journal of Mechanical Engineering Science 13(5):316-329 (1971).

Standards:

• ISO 8855:2011 «Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary» (canonical axis convention).
• EN 17128:2020 «Personal light electric vehicles — Safety requirements and test methods» (§5.1 max rider, §6.4 frame impact, §6.5 frame fatigue, §7.6 curb-mount test).
• ISO 4210-3:2014 «Cycles — Safety requirements for bicycles — Part 3: Common test methods» (adjacent reference for frame fatigue).
• UNECE Regulation 78 «Uniform provisions concerning the approval of vehicles of category L with regard to braking» (motorcycle reference).
• 49 CFR 571.122 FMVSS 122 (USA motorcycle brake reference).

Educational sources:

• MSF (Motorcycle Safety Foundation) «Basic RiderCourse Rider Handbook» (current edition) — braking technique lesson on weight transfer.
• Wikipedia «Bicycle and motorcycle dynamics» — accessible overview of load-transfer formulas and single-track vehicle dynamics.

Empirical data:

• CPSC «E-Scooter and E-Bike Injuries Soar» 2024 release — incident mechanisms including forward-pitchover.
• Bosch «Studie zur Wirksamkeit von eBike ABS» 2019 whitepaper — emergency braking field-test data.
• ADAC «Antiblockiersystem für E-Bikes» 2020 test review — pitchover frequency in emergency braking without ABS.