Relative Velocity Calculator: River Crossing and Aircraft Wind Correction Angle

Boats in currents and aircraft in winds.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose a boat in a river or an aircraft in a wind.

Enter the speeds and the river width, or the track and the wind.

The calculator gives the headings, the times, the drift and the ground speed.

Formulas used

  • \sin\theta = \frac{v_c}{v_b}
  • t = \frac{W}{\sqrt{v_b^2 - v_c^2}}
  • WCA = \arcsin\frac{w\sin\beta}{v_a}

Worked example

With the default numbers in the calculator above:

  1. Heading straight across: the time to cross is the width over the boat speed: 33.333 s
  2. Heading straight across: how far the current carries the boat downstream: 50 m
  3. Heading straight across: the ground speed and the path angle: 3.3541 m/s at 26.57 degrees downstream of straight across
  4. To land directly opposite: head upstream at this angle from the line straight across: 30 degrees
  5. Speed across the river in that case: 2.5981 m/s
  6. Time to cross in that case: 38.49 s

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? An aircraft in a wind.

  1. Wind correction angle (the angle the nose is pointed into the wind): 11.537 degrees
  2. Heading to steer (the track plus the wind correction): 101.54 degrees true
  3. Ground speed along the track: 244.95 km/h
  4. Headwind component (positive is a headwind) and crosswind component: 0 km/h headwind and 50 km/h crosswind

Common questions

How do I cross a river to land directly opposite?

Point the boat upstream at an angle whose sine is the current speed over the boat speed.

How do I cross a river in the shortest time?

Head straight across. The current carries you downstream but does not change the time to cross.

What is a wind correction angle?

The angle between the track and the heading, to cancel the sideways push of the wind.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any first-year physics text (relative motion). For flight planning use approved navigation tools.

Need a calculator we do not have?

Tell us what you would like to calculate. We read every request and build the most asked-for ones.

We store your request (and your email if you give it) to decide what to build. We do not store the numbers you type into calculators.

Embed this calculator on your own page

Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.

Need this drawn, designed or checked?

Drafting Central is a mechanical engineering and drafting business working with customers across Australia and around the world. A calculator gives you the numbers; we can turn them into drawings and designs.

Need help with a real project?

Talk to Drafting Central →

← All engineering calculators