1. Purpose & Methodology

This document establishes the emergency braking force calculations for a 6,000-gallon liquid tanker at 52.5% fill, the fill level independently established as the worst case for surge force (see Why Partial Loads Are the Most Dangerous), using the same formula documented in full on How We Calculate Surge Force at Any Fill Level or Tank Size. It provides the citable engineering basis for the braking argument used in LSC marketing and email materials.

Two things scale differently here, and it matters which is which. Liquid density scales surge force linearly: this follows from F = ma at a fixed volume and deceleration profile, a reasonable first-principles assumption. Fill level does not scale linearly; it follows fill × (1 − fill), zero surge at empty, zero at full, a peak at the middle, a documented phenomenon independently established across multiple studies (Yan & Rakheja, 2009; Kolaei, Rakheja & Richard, 2014 to 2017; Biswal et al., 2006). Budwig's own test happened to run at 80% fill, so a simpler linear-in-mass approximation coincidentally matches the correct formula at that one point, but diverges from it everywhere else, and would not reproduce the fill × (1 − fill) peak that the partial-loads finding depends on. This document uses the correct formula throughout, not the coincidental approximation.

2. Reference Scenario & Assumptions

None of these four values are fixed properties of the physics, they're reference values chosen for a single, repeatable, citable scenario. All four are genuinely editable inputs on the live calculator (Combined Empty Weight, tank capacity, fill level, and coefficient of friction are all user fields, id="emptyWt" defaults to 33,000 but is not fixed). 33,000 lbs and 0.60 CoF are used here because they match the calculator's own defaults and the site's other reference materials, not because they're the only correct values.

This differs from the original draft of this document, which derived vehicle weight by subtracting the tank's empty-space weight from the 80,000 lb legal maximum. That approach implies a different tare weight for each liquid carried, physically inconsistent for one vehicle, and was replaced with the fixed 33,000 lb reference used elsewhere on this site.

3. Scaled Surge Forces at 52.5% Fill

Using K = 3.598 × (density ÷ 7.10), and Surge = K × 47,000 × (capacity ÷ 6,000) × fill × (1 − fill) ÷ 0.20 × (CoF ÷ 0.60), calibrated to reproduce Budwig's measured result (26,480 lbf at 80% fill, 1,000 gallons, 40 mph, CoF 0.60) to within 0.1%.

4. Full Braking Force Equation

GVW = 33,000 lb tare + liquid weight (capacity × density × fill). Brake capacity = GVW × 0.60 CoF. Total braking demand = GVW + surge force. Braking-required multiple = total demand ÷ brake capacity, the same definition used throughout this site (total braking demand divided by braking capacity, not divided by the legal GVW limit, which is a separate informational comparison).

Even with Surge Busters installed, total demand still exceeds available brake capacity by roughly 1.9× across all three liquids, the residual 3.3% of a very large starting force is still a meaningful number. The difference is the gap it closes: from an 8–10× deficit to well under 2×.

→ See the chart: Peak Braking Demand (PDF)

5. Equivalent Static Weight

What static vehicle weight at 0.60 CoF would generate the same braking demand as the surge force alone (without Surge Busters), expressed as a percentage of the federal 80,000 lb GVW limit, gives a sense of scale for a force that has no static-weight equivalent in the real vehicle.

6. Caveats & Limitations

• The fill × (1 − fill) function is an engineering representation of a confirmed phenomenon (zero surge at empty and full, a peak near the middle), not a formula published in the cited studies, and the 47,000 lb reference payload and 0.20 divisor are calibrated to reproduce Budwig's one measured result, not derived from it independently.
• The Budwig model is explicitly described as a conservative first-iteration estimate designed to overestimate surge forces (p. 6). These results inherit that conservative bias.
• Density values are representative at standard temperature and vary by grade and temperature: fuel oil No. 2 at 7.10 lbs/gal, water at 8.34 lbs/gal (ASTM, 60°F), UAN fertilizer at 11.06 lbs/gal.
• All calculations use a 0.60 coefficient of friction, matching the Budwig test conditions and representing typical emergency braking on dry pavement. Wet pavement (CoF ≈ 0.30–0.40) roughly doubles the multiples shown here.
• Speed is not a variable in this model; emergency-braking deceleration is friction-limited, not speed-limited. See the full explanation.
• The 96.7% reduction (3.3% residual) is Budwig's single fore-to-aft tilt-table measurement. The cancellation mechanism itself is not direction-limited by construction, but the exact percentage side-to-side has not been separately measured.

7. Citation Format