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Slope Recovery Calculator

2026-09-27 6 min

Downhill slide force and winch hold requirement for a vehicle on a grade.

Downhill Force
1881 lb
Hold Required
0 lb
0 means tires/brakes hold alone

Calculator

Vehicle Weight(lb)
lb
Slope Angle(deg) Help
deg

Hill angle in degrees

Friction Coefficient Help

Loose dirt ~0.4, rock ~0.7

Results update live as you type

Live statistics

Downhill Force

1881 lb

Hold Required

0 lb

0 means tires/brakes hold alone

Results

Optimal

Downhill Force

1881lb

Hold Required

0lb

0 means tires/brakes hold alone

Planning estimate from standard automotive formulas. Validate with dyno, timeslip or datalog data when precision matters.

Visualizations

Results overview

1,881Downhill Force
0Hold Required

Hold Required vs. Vehicle Weight

Hold Required

0lb
015,000

Formula

Compares the sliding component of weight against available tire friction to find the winch assist needed.

Downhill = W x sin s; hold = max(0, downhill - friction x W x cos s)

Alternative Form

Negative hold means the grade holds itself — brakes alone suffice

Variables

SymbolNameUnitDescription
sSlope angledegConverted to radians for sin/cos
uFriction coefficientWet clay 0.2, dirt 0.4, dry rock 0.7

Explanation

Friction fights slide with the cosine (grip) while gravity pulls with the sine — steep and slick means the winch does the holding.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Record the inputs.

Vehicle Weight:5500 lb
Slope Angle:20 deg
Friction Coefficient:0.4
Result: 3 inputs ready
Step 2

Apply the formula.

Downhill = W x sin s; hold = max(0, downhill - friction x W x cos s)
Result: Primary result = 0 lb
Step 3

Read every derived output.

Downhill Force:1881 lb
Hold Required:0 lb
Result: Hold Required = 0 lb
Final Answer
1881

Worked Examples

See how the calculator works with different scenarios.

Scenario

Holding a rig on a dirt descent.

Inputs

Weight:5,500 lb
Slope:20 deg
Friction:0.4

Calculation

Downhill = 1,881 lb; grip = 2,067 lb; hold = 0 lb

Result

No winch hold needed.

Interpretation

Tires and brakes hold it; chock and spot normally.

Understanding Your Result

Your Result: Downhill Force: 1881 lb

Typical range: Mild dry grades hold alone; wet or steep grades need 1,000-5,000 lb of belay.

What This Means

How much restraint keeps the vehicle from sliding.

Why It Matters

Decides whether brakes suffice or a winch must belay the descent.

Professional Interpretation

Treat the primary result as a planning estimate, then validate on a dyno, at the track, or with logged sensor data. If measured numbers disagree by more than ~10%, re-check inputs (units are the usual culprit) before changing parts.

Recommendations

  • •Double-check units on every input before trusting the result
  • •Compare against the worked example below to sanity-check magnitude
  • •Validate with measured data (dyno, timeslip, datalog) when it matters

Learn — fuel economy, deeply

Slope holding is gravity sliding versus tire grip.

1 · Where the gallon goes (energy path)

Engine heat

60–70% lost

Coolant + exhaust carry most energy away. Hybrids recover some via Atkinson cycle + regen.

Driveline

5–15% lost

Transmission, differential, accessories. CVTs and 8–10 speed autos lose less.

Aero drag

∝ v²

Doubles from 55→78 mph. Roof boxes hurt more than trunks.

Rolling + brakes

10–20%

Tires, weight, stops. Regen braking (hybrid/EV) reclaims city braking energy.

4 · Measure like a pro (the 3-tank protocol)

  1. Fill to first click at the same pump, record the odometer (Tank 0).
  2. Drive normally for 2–3 tanks; always refill to first click at the same pump.
  3. MPG = total miles ÷ total gallons across all tanks — averaging kills pump-click noise.
  4. Cross-check with the trip computer; a persistent >10% gap means the computer needs calibration — or the car needs service.
  5. Log with an OBD-II dongle for per-trip MPG if you want to isolate commute vs. highway behavior.

Practical Tips

  • •Chock wheels before unhooking anything
  • •Belay descents steeper than friction allows
  • •Re-check friction when rain or ice arrives

Common Mistakes

Mixing units (inches with mm, psi with kPa)
Convert every input to the unit shown on its field before calculating.
Trusting a single output blindly
Cross-check with the worked example and, when it matters, a dyno or datalog.

Assumptions

This calculator makes the following assumptions to provide estimates:

Steady-state model: Formulas assume stabilized conditions; transients, heat soak and traction limits are excluded.
Standard factors: Empirical constants (BSFC, VE, drivetrain loss) use typical values — your combination may differ.

Limitations

Be aware of these limitations when using this calculator:

Estimate, not measurement: Predictions carry real-world scatter of roughly ±5–15% depending on the model.
No transient effects: Shift time, wheelspin, spool lag and heat soak are not modeled here.

Frequently Asked Questions

Answers to common questions about this calculator.

When does hold read zero?
When tire friction exceeds the downhill slide force — the grade self-holds and the winch is backup only.
What friction value should I use?
Dry rock ~0.7, dirt ~0.4, wet clay ~0.2, ice ~0.1. Downgrade one step in the rain.

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Related Guides

Deepen your understanding with these educational resources.

Glossary

Technical terms used in mortgage calculations explained in plain language.

MPG
Miles per gallon. Distance travelled per gallon of fuel; higher is better. US gallon = 3.785 L.
L/100 km
Litres consumed per 100 kilometres; lower is better. Standard metric efficiency unit.
MPGe
Miles per gallon-equivalent. EV metric: miles travelled on 33.7 kWh (energy of 1 gal of gasoline).
CAFE
Corporate Average Fuel Economy — US fleet-average efficiency standard enforced by NHTSA.
Rolling resistance
Energy lost deforming tires as they roll. Low-pressure or wide tires raise it.
Aerodynamic drag
Air resistance growing with the square of speed — why highway MPG falls fast above 60 mph.
Hypermiling
Driving techniques (coasting, steady speed, anticipation) that maximise real-world MPG.
OBD-II
On-board diagnostics port. Scanners and dongles read live MPG, fuel trim and fault codes.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

EPA Fuel Economy Testing (40 CFR Part 600)CAFE — Corporate Average Fuel Economy Standards (NHTSA)WLTP — Worldwide Harmonised Light Vehicle Test ProcedureSAE J1321 / J1711 — Fuel consumption test proceduresISO 2575 — Road vehicles symbols & efficiency markings

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