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ENGINEERING CALCULATORS

Moving force, slope & power calculator

Engineering calculators (Beta)

Find the required moving force and power from mass, slope, friction and speed.

Inputs

Choose units and enter numbers. Full-width digits and fractions such as 1/8 or 1 3/8 are accepted. Changing a unit converts the entered value.

Results

Reference calculation only. Results do not certify suitability for an actual design or its safety.

Diagram

Inputs: select a blue symbol to edit Results: red-orange values and lines

Formula and applicability

N = mg cosθ, F = ma + mg sinθ + μk N, Fstart = max(0, mg sinθ + μs N), Pdrive = Fv/η (F≥0), Pbrake = −Fv (F<0), Twheel = Fr

Displayed values are rounded. Diagrams illustrate the calculation conditions. Initial material and fluid properties are examples; replace them with values for the actual material, temperature and conditions.

Reference
Using this information as a reference

Equations assume particular loads, supports and deformation ranges. Check inputs, units and the applicability of each equation. Diagrams explain conditions; they are not manufacturing drawings or proof of safety.

Material values are typical values or reference ranges, not certified product properties or ready-to-use design allowables. They vary with standards, product form, dimensions, temper and temperature. Check the specifications and inspection certificates for the actual product.

Displayed safety factors and checks apply only to the supplied inputs and calculation model. They do not automatically establish the safety of a complete design, including code compliance, service life, fatigue or joints. For actual design, manufacture and use, separately verify applicable regulations and standards, product specifications, and the necessary tests and engineering review.

この計算で求められること

何kgのものを、どの勾配・摩擦・速度で動かすかから必要な力と動力を求めます。

入力・結果・適用条件を確認する

選択した形状・計算方法により、使う項目は変わります。実際の計算は上の図と入力欄で行えます。

主な入力

  • 移動する質量 m (kg / g / mg)
  • 進行方向の勾配 θ(下りは負) (° / rad / % grade)
  • 動摩擦係数 μk (—)
  • 静摩擦係数 μs(始動用) (—)
  • 進行方向の加速度 a(減速は負) (m/s² / mm/s² / g)
  • 進行速度 v (m/s / km/h / mm/s)
  • 駆動系の効率 η (% / fraction / ‰)
  • 駆動輪・ドラムの半径 r (mm / cm / m)

得られる結果

  • 走行中の必要駆動力 F(負は制動) (N)
  • 正方向へ動き始めるための力(加速分なし) (N)
  • 正方向駆動の必要入力動力 (W)
  • 吸収が必要な制動動力 (W)
  • 駆動輪・ドラムでのトルク(符号付き) (N·m)
  • 垂直抗力 N (N)
  • 進行方向と逆向きの重力成分(符号付き) (N)
  • 走行中の摩擦抵抗 μk N (N)
  • 駆動力の換算(kgf。質量kgではありません) (kgf)
  • 勾配の角度 (°)
  • 勾配(高さ/水平距離×100) (%)

計算式の概要

N = mg cosθ, F = ma + mg sinθ + μk N, Fstart = max(0, mg sinθ + μs N), Pdrive = Fv/η (F≥0), Pbrake = −Fv (F<0), Twheel = Fr

直線上を正方向へ走行し、駆動力は路面と平行に作用するモデルです。勾配は角度・rad・%を切り替えられます(5%は5°ではありません)。μは接触条件に合わせて入力し、このモデルではμs≥μkです。始動欄は静摩擦の境界で、加速分は含みません。走行中は動摩擦を使用します。駆動力が負なら正方向へ進むために制動が必要です。制動の回生効率は扱いません。車輪の転がり抵抗・空気抵抗・回転慣性・伝達比は別途。トルクは駆動輪での値で、モーター軸ではありません。

現在選択中の方法には、操作欄の「計算式・適用条件」を使ってください。参考計算であり、設計全体の安全性を保証するものではありません。

関連する計算

What this calculator does

Find the required moving force and power from mass, slope, friction and speed.

Inputs, outputs and applicability

The selected model determines which of these inputs and outputs apply. Use the working diagram and input panel above to calculate.

Inputs

  • Moving mass m (kg / g / mg)
  • Route slope θ (negative downhill) (° / rad / % grade)
  • Kinetic friction coefficient μk (—)
  • Static friction coefficient μs (breakaway) (—)
  • Acceleration a (negative when decelerating) (m/s² / mm/s² / g)
  • Forward speed v (m/s / km/h / mm/s)
  • Drive efficiency η (% / fraction / ‰)
  • Drive wheel / drum radius r (mm / cm / m)

Calculated results

  • Required running drive force F (negative: brake) (N)
  • Positive breakaway force (excluding acceleration) (N)
  • Required positive-drive input power (W)
  • Mechanical braking power to absorb (W)
  • Wheel / drum torque (signed) (N·m)
  • Normal force N (N)
  • Opposing gravity component (signed) (N)
  • Running friction resistance μk N (N)
  • Drive force equivalent (kgf, not mass kg) (kgf)
  • Slope angle (°)
  • Grade (rise / horizontal run × 100) (%)

Formula overview

N = mg cosθ, F = ma + mg sinθ + μk N, Fstart = max(0, mg sinθ + μs N), Pdrive = Fv/η (F≥0), Pbrake = −Fv (F<0), Twheel = Fr

Straight positive-direction travel with drive force parallel to the surface. Switch between degrees, radians and grade percent (5% is not 5°). Enter coefficients for the actual contact; this model requires μs≥μk. Breakaway is the static-friction threshold without acceleration; running force uses kinetic friction. Negative drive force requires braking during forward travel. Regeneration efficiency, wheel rolling resistance, drag, rotational inertia and gearing are excluded. Torque is at the drive wheel, not the motor shaft.

The displayed formula and conditions in the working panel apply to the currently selected model. Reference calculation only; it does not certify a complete design.

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数値の感覚を、図と動きで確かめる

説明用の別モデルです。適用条件を確認してください。数値は自動転記しません。

See the idea in diagrams and motion

A separate explanatory model. Check its assumptions; values are not transferred.