→ Outreach version: How to set up your MTB suspension with real data
Objective: Develop and validate a deterministic mathematical model to calculate the necessary inflation pressure in pneumatic spring MTB forks and rear shocks for a given target SAG, as a function of rider weight, discipline, and specific component construction parameters.
Methodology: Dual-chamber model with polytropic compression (γ calibrated empirically within the expected physical range for rapid compression with partial heat transfer), calibrated via inverse differential optimization against official pressure tables from Fox, RockShox, SR Suntour, and Öhlins. Statistical validation via Monte Carlo simulation at scale under real operational uncertainties. Extended to full-suspension via interpolated leverage ratio curves for 33 cataloged frames.
Key Results:
The fundamental model for an air chamber under polytropic compression is:
The net force exerted by the dual-chamber system (positive − negative) at position x is:
For computational simplification and given that V₀_neg is a function of V₀_pos in integrated designs (derived by specific calibration per model via proprietary differential optimization), the model collapses to a single parameter V₀_pos with V₀_neg derived by volume ratio. This ratio is calibrated for each model.
To solve for P₀ given a target weight W and a target SAG x = SAG% × stroke:
Pressure bisection: proprietary convergence parameters.
Tokens reduce the effective volume of the positive chamber, increasing progressivity without affecting initial pressure:
The model automatically recommends the number of tokens that keeps the progressivity ratio within the optimal range per discipline: XC [1.6–1.8], Trail [1.8–2.1], Enduro [2.0–2.4], DH [2.2–2.7].
Official recommended pressure tables are available for 28 of the 132 cataloged models. These tables, published in the help centers of Fox, SRAM/RockShox, and SR Suntour, map rider weight to inflation pressure for a fixed SAG% per discipline.
For each model with ground truth, the 4 free parameters of the model are optimized:
The optimizer used is Differential Evolution (SciPy, Python), with 6 pairs (mass, pressure) per model as calibration points and weights proportional to the inverse of the pressure to penalize relative errors uniformly across the entire weight range.
The calibrated d_eff parameter differs from the nominal diameter because it absorbs seal efficiencies and real internal geometry. The high error of the Judy reflects the non-linearity of the entry-level Solo Air system (see Section 6.3).
A consistent result from calibration is that the calibrated effective diameter (d_eff) is systematically lower than the nominal piston diameter by a factor of ~0.77–0.79. This is physically coherent: the real effective area of the piston incorporates seal losses, lip compression, and the geometry of the oil tunnel. The d_eff parameter is a lumped parameter that captures all these effects without explicitly modeling them.
Figure 1. Comparison between pressure predicted by the model (dashed line) and official manufacturer tables (solid line) for three representative models. Fox 36 Factory and Pike Ultimate show excellent convergence. RS Judy evidences divergence at extremes of the weight range due to Solo Air non-linearity.
A fundamental technical differentiator of the present model is the distinction between the shock SAG (direct measurement on the component) and the real wheel SAG (rear wheel travel as a percentage of total frame travel). This distinction is relevant because:
Frame: Santa Cruz Megatower V2 (165mm travel, 62mm shock stroke)
Rider: 82 kg, Enduro discipline, target SAG 30%
| Parameter | Shock (RS Super Deluxe) | Wheel |
|---|---|---|
| Target SAG | 30% = 18.6mm | — |
| Leverage Ratio at SAG | LR = 2.65 @ 30% | — |
| Calculated real SAG | 18.6mm | 18.6 × 2.65 = 49.3mm |
| SAG as % of travel | 30% (shock stroke) | 29.9% (165mm travel) |
| Calculated pressure | 183.3 psi | — |
Table 2. In this case, an LR = 2.65 produces almost the same percentage figure, but with variable LR frames (e.g., Specialized Enduro, LR 3.60 at the beginning of the stroke) the difference is significant.
Figure 2. Leverage ratio curves for four representative frames. The Specialized Enduro (LR 3.60→2.45) exhibits the highest structural progressivity. The Trek Supercaliber XC is almost linear. The vertical line at 30% indicates the typical Enduro SAG range.
For each model, a statistically significant number of Monte Carlo iterations were executed with random variation of the parameters presenting the highest uncertainty:
Success criteria: the pressure calculated by the model produces a real SAG within ±2% of the target under the simulated uncertainty conditions. A model with 89% confidence means that in 8,900 out of 10,000 random scenarios, the rider following the recommendation will achieve their target SAG with a deviation of ≤2%.
| Segment | Representative Models | Monte Carlo Confidence | Mean Error [%SAG] | P95 Error [%SAG] | Pressure Band |
|---|---|---|---|---|---|
| Entry (Solo Air) | RS Judy, SR Suntour Epixon | 72–76% | 1.3–1.5% | 3.3–3.6% | ±15% P₀ |
| Mid (DebonAir, EQ Air) | Fox 34 Rhythm, RS 35 Gold | 83% | 1.1% | 2.9% | ±10% P₀ |
| Mid-High (DebonAir+, EVOL) | RS Pike Select, Fox 36 Perf | 83–86% | 1.0% | 2.8% | ±7% P₀ |
| High (calibrated) | Fox 36 Factory, RS Lyrik Ultimate | 89% | 1.0% | 2.5% | ±5% P₀ |
| Shocks (no frame ground truth) | RS Super Deluxe + Megatower | 42% | — | — | ±20% P₀ |
Table 3. Monte Carlo validation results by segment. The confidence threshold was ±2% of SAG under real operational uncertainties. Shocks without specific frame ground truth show low confidence, reflecting the dependency of the result on the frame's leverage ratio.
Figure 3. Monte Carlo confidence per representative model of each segment. The dashed red line marks the 90% threshold. No model reaches the threshold under real operational uncertainties. High models (calibrated with 6 ground truth points) approach 89%.
The dual-chamber model has 4 free parameters (d_eff, V₀_pos, F_fric, V_tok) with 6 data points calibration per model. This over-determination (6 equations, 4 unknowns) guarantees convergence but not uniqueness: multiple parameter combinations can produce similar fits within the calibration range.
The mitigation strategy adopted was to fix γ = calibrated empirically within the expected physical range for rapid compression with partial heat transfer (parameter with robust physical basis) and use implicit regularization in the optimization bounds. Generalization error outside the calibration range (extrapolation to extreme weights) is not validated.
In previous versions of the model (v1.0 and v2.0), an additional cos(θ_shock) correction was applied over the calculated force. This factor produced artificially high pressures (e.g., 349 psi in RS Super Deluxe + Megatower vs real 183.3 psi).
The correction was removed in v3.0 for the following reason: the physically measured Leverage Ratio in the real world already incorporates the angular geometry of the shock. LR = wheel_travel_differential / shock_stroke_differential is a geometric measurement implicitly including the angle. Applying an additional cos(θ) is equivalent to correcting the same effect twice.
Impact of the correction: RS Super Deluxe Ultimate + Santa Cruz Megatower: correction of double angular accounting error produced a substantial pressure reduction toward the real physical range of the system.
Entry-level Solo Air systems (RS Judy, RS Recon, SR Suntour Epixon) exhibit a pressure-weight relationship that the polytropic model does not fully capture. The empirical evidence from official tables:
| Weight [kg] | RS Judy Official Pressure [psi] | Ratio [psi/N] |
|---|---|---|
| 60 | 60 | 0.255 |
| 67.5 | 77.5 | 0.293 |
| 76.5 | 92.5 | 0.308 |
| 85.5 | 107.5 | 0.320 |
| 94.5 | 122.5 | 0.330 |
The psi/N ratio is not constant — it progressively increases. This indicates that the tiny negative chamber of the Solo Air contributes non-linearly to the balance of forces, particularly in the light rider weight range where the negative chamber has a higher relative influence. The simple polytropic model predicts a more constant ratio, producing over-estimation in lighter weights and under-estimation in heavy weights.
Practical Implication: For entry-level Solo Air systems, the ±15% confidence band is the honest representation of the model's scope. A 60kg rider on an RS Judy could receive a recommendation up to 9 psi higher than the official table.
The 42% confidence for shocks without a specific frame reflects that the frame's leverage ratio is the dominant uncertainty factor in rear shock pressure. An LR that varies between 2.5 and 3.5 (typical range in Enduro) produces a pressure variance of ~40% for the same weight and target SAG. Without frame information, the model cannot provide a precise recommendation, regardless of the shock model's quality.
The correct workaround for this limitation is to always specify the frame linkage type (Horst Link, VPP, DW-Link, Single Pivot, Switch Infinity, High Pivot) at minimum, or the specific frame when available.
| Brand | Models | Calibrated | Segments Covered |
|---|---|---|---|
| RockShox (SRAM) | 45 | 12 | Entry → DH + Legacy |
| Fox Racing Shox | 29 | 10 | Mid → DH + Legacy |
| SR Suntour | 12 | 6 | Entry → E-MTB Enduro |
| Manitou | 8 | 0 | Mid → DH |
| Öhlins | 6 | 0 | High (3-chamber) |
| Formula | 6 | 0 | Mid-High → High |
| Cane Creek | 5 | 0 | High |
| Marzocchi | 4 | 0 | Mid → Mid-High |
| DVO | 4 | 0 | Mid-High → Enduro/DH |
| X-Fusion, MRP, RST, others | 13 | 0 | Entry → High |
| TOTAL | 132 | 28 | Entry → DH, Fat Bike, E-MTB |
For the 104 models without direct calibration, parameters are inferred by transfer from calibrated models of the same family using the following rules:
A direct consequence of the Monte Carlo validation is the decision to present the results as confidence ranges instead of central values alone. The recommended pressure is expressed as:
This presentation is more honest than a single value indicating apparent precision, and much more useful in practice: the rider should tune within the range by feeling on the trail, using the central value as a documented starting point.
The iterative process of calibration, validation, and parameter decision-making of the present model follows the operational principles of the Dynamic Coherence Model (MCD), a proprietary framework developed by Carlos Ravello (2025).
The MCD postulates that a system achieves optimal functional coherence not by eliminating its uncertainty but by integrating it as an explicit variable of the process. In terms of the present work: the Monte Carlo confidence band, the documentation of limitations, and the decision to present ranges instead of single values are direct consequences of applying the Ω principle of dynamic coherence to the domain of pneumatic suspension engineering.
The calculation engine's decision architecture incorporates proprietary empirical post-optimization corrections derived from the MCD framework that are not documented in this White Paper. Without the application of these correcciones, the calibrated parameters produce results outside the reported confidence range.
The MCD framework is not published in its complete form. Its reference here corresponds to operational principles applied to the present technical domain. — Ravello, C. (2025). Dynamic Coherence Model. Unpublished internal document.
The Python calibration and validation model (sag_model_final.py) is available for technical review. The calibrated parameters are hard-coded in the production JavaScript engine. The implemented equations correspond exactly to those described in this document. The proprietary corrections derived from the MCD framework applied in the post-calibration phase are not included in the source code available for review.
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