Calculation
v' = v·√(sin²α+k²cos²α); α' = atan2(sinα,kcosα)
A smooth wall changes only velocity normal to its surface; the parallel component remains unchanged during frictionless impact.
Schiefer Stoß gegen starre glatte Wand · v'n=−k·vn, v't=vt
Calculate Rebound from an Oblique Wall Impact
A smooth wall changes only velocity normal to its surface; the parallel component remains unchanged during frictionless impact.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Rebound speed v′ — Magnitude of velocity immediately after contact in m/s, combining unchanged tangential and restitution-reduced normal components.
- Outgoing angle α′ to wall normal — Post-impact velocity angle to the wall normal on the rebound side; 0° is straight rebound, 90° tangential departure. Undefined when the body stops.
- Incoming speed v — Speed magnitude immediately before wall contact from measurement or motion calculation; positive.
- Incidence angle α to wall normal — Angle between incoming velocity and wall normal: 0° head-on, 90° grazing limit. Do not measure from the wall surface.
- Coefficient of restitution k — Ratio of rebound to incoming normal speed from a relevant impact test; 0 perfectly plastic, 1 ideally elastic. Not a universal material constant.
Example
A body hits at v=10 m/s and α=30° to the wall normal. At k=0.6, tangential speed remains 5 m/s and normal rebound speed is 5.196 m/s, giving v′=7.211 m/s and α′=43.898°.
Assumptions and limits
Point-like body against a much heavier stationary rigid smooth wall; frictionless central contact without rotation. Restitution affects only the normal component; contact force, friction, spin, deformation and multiple impacts are excluded. α=90° is the grazing limit without normal impulse.
Understand Oblique impact against a smooth wall
A body strikes a wall obliquely. This calculator gives its speed and angle immediately after rebound when the wall is smooth and practically stationary.
What does this quantity describe?
Incidence angle α is measured from the wall normal, not from its surface. Before impact, normal speed is vn=v·cosα and tangential speed vt=v·sinα. With smooth frictionless contact, impact impulse acts only normal to the wall: the normal velocity reverses with factor k, while tangential velocity remains unchanged. The outgoing magnitudes are v′=v·√(sin²α+k²cos²α) and α′=atan2(sinα,kcosα). k is restitution coefficient between 0 and 1.
Formula and variables
v' = v·√(sin²α+k²cos²α); α' = atan2(sinα,kcosα)
Before impact: vn=vcosα, vt=vsinαAfter impact: v′n=−k·vn, v′t=vtMagnitude: v′=v√(sin²α+k²cos²α)Outgoing angle to normal: α′=atan2(sinα,kcosα)
| Symbol / input | Meaning |
|---|---|
| Rebound speed v′ | Magnitude of velocity immediately after contact in m/s, combining unchanged tangential and restitution-reduced normal components. |
| Outgoing angle α′ to wall normal | Post-impact velocity angle to the wall normal on the rebound side; 0° is straight rebound, 90° tangential departure. Undefined when the body stops. |
| Incoming speed v | Speed magnitude immediately before wall contact from measurement or motion calculation; positive. |
| Incidence angle α to wall normal | Angle between incoming velocity and wall normal: 0° head-on, 90° grazing limit. Do not measure from the wall surface. |
| Coefficient of restitution k | Ratio of rebound to incoming normal speed from a relevant impact test; 0 perfectly plastic, 1 ideally elastic. Not a universal material constant. |
Choose the inputs correctly
v is positive incident speed in m/s immediately before contact from measurement or prior motion calculation. α is incidence angle to wall normal in degrees, 0° head-on and 90° grazing. k is dimensionless ratio of normal rebound to incident speed from a comparable impact test; k=0 gives no normal rebound and k=1 ideal elasticity. v′ is outgoing speed magnitude in m/s and α′ is outgoing angle to the normal in degrees. Select the desired result above the fields.
How to use the calculator
Draw the wall normal and measure α from it to the incoming velocity vector. Enter v and a restitution coefficient for this contact pair and speed range. Read v′, then α′. At α=0 and k=0 the body stops and no outgoing angle exists.
Worked example
At v=10 m/s, α=30° and k=0.6, vt=10·sin30°=5 m/s and normal rebound speed k·vn=0.6·10·cos30°=5.196 m/s. Thus v′=√(5²+5.196²)=7.211 m/s and α′=atan2(5,5.196)=43.898°.
Understand the result and units
With k=1, α′=α and speed is unchanged. Lower k makes the outgoing path more parallel to the wall because tangential velocity remains while normal velocity falls. At grazing α=90°, no normal impact occurs in this ideal model.
Internally v uses m/s and α converts to radians; k is dimensionless. Output uses m/s or degrees. atan2 handles the tangential limiting case when k=0.
Typical applications
Initial estimates of rebound paths for smooth balls, particles or test objects against a massive surface without spin or friction.
Assumptions, limits and common mistakes
Point-like body, rigid stationary smooth wall, central frictionless impact without rotation. Wall compliance, friction, spin, roughness, impact duration and contact force are excluded. Restitution must be determined for the actual contact and speed range.
Common mistake: Do not measure incidence angle from the wall surface; 30° to the wall is 60° to its normal. Multiply only normal velocity by k, not tangential velocity. Do not read α′ as 0° if the body comes to rest.
Frequently asked questions
What is “Oblique impact against a smooth rigid wall” used for?
Initial estimates of rebound paths for smooth balls, particles or test objects against a massive surface without spin or friction.
Where do the input values come from?
v is positive incident speed in m/s immediately before contact from measurement or prior motion calculation. α is incidence angle to wall normal in degrees, 0° head-on and 90° grazing. k is dimensionless ratio of normal rebound to incident speed from a comparable impact test; k=0 gives no normal rebound and k=1 ideal elasticity. v′ is outgoing speed magnitude in m/s and α′ is outgoing angle to the normal in degrees. Select the desired result above the fields.
What does the result not cover?
Point-like body, rigid stationary smooth wall, central frictionless impact without rotation. Wall compliance, friction, spin, roughness, impact duration and contact force are excluded. Restitution must be determined for the actual contact and speed range.