Calculator Inputs
Formula Used
The main formula is:
f = N / t
Here, f is tail beat frequency in hertz. N is the number of complete tail beats. t is observation time in seconds.
Swim speed is calculated with:
U = d / t
The Strouhal number is calculated with:
St = f × A / U
Here, A is peak-to-peak tail amplitude. U is swimming speed. The calculator also returns period, angular frequency, stride length, amplitude ratio, and tail tip motion estimates.
How to Use This Calculator
- Count complete left-right-left or right-left-right tail cycles.
- Choose direct time or video frame mode.
- Enter distance, fish length, and tail amplitude.
- Add uncertainty if your video or count is rough.
- Press calculate to view frequency and motion results.
- Use CSV or PDF buttons to save the output.
Example Data Table
| Trial | Tail Beats | Time | Distance | Fish Length | Amplitude | Frequency | Strouhal Number |
|---|---|---|---|---|---|---|---|
| Steady swim | 30 | 10 s | 0.85 m | 12 cm | 3.2 cm | 3.000 Hz | 1.129 |
| Slow cruise | 18 | 12 s | 0.60 m | 14 cm | 2.5 cm | 1.500 Hz | 0.750 |
| Fast burst | 45 | 8 s | 1.40 m | 11 cm | 3.8 cm | 5.625 Hz | 1.221 |
Fish Tail Beat Frequency in Swimming Physics
Why Tail Motion Matters
Fish swimming is a useful topic in physics. The tail works like an oscillating propulsor. It pushes water backward. The fish then moves forward. Tail beat frequency helps describe that motion. It tells how many complete tail cycles happen each second.
Using Video Observations
A video makes this measurement easier. You can count complete tail beats frame by frame. You can also measure the duration from frame count and frame rate. This reduces timing error. It also helps when fish move quickly.
Speed and Body Length Scaling
Raw speed is useful. Yet fish size also matters. A small fish and a large fish can have the same speed. Their swimming effort may still differ. Body lengths per second solves this problem. It scales speed by fish length.
Amplitude and Strouhal Number
Tail amplitude describes side motion. Large amplitude can increase water movement. It may also increase energy cost. The Strouhal number links frequency, amplitude, and speed. It gives a compact view of swimming kinematics.
Reading the Result
A higher frequency means faster tail cycling. A shorter period means each cycle takes less time. Angular frequency shows the same motion in radians per second. Tail tip velocity and acceleration estimate the intensity of tail movement.
Practical Notes
Use steady swimming clips when possible. Avoid turns, starts, and stops. Measure peak-to-peak tail amplitude from the leftmost tail tip position to the rightmost position. Keep units consistent. The calculator converts common length and time units automatically.
FAQs
1. What is fish tail beat frequency?
It is the number of complete tail beat cycles per second. The unit is hertz. One complete cycle usually means the tail returns to the same side position after moving through both sides.
2. What is a complete tail beat?
A complete tail beat is one full oscillation. For example, left to right and back to left can be counted as one full cycle.
3. Can I use video frames?
Yes. Select video frame mode. Enter the number of observed frames and the frame rate. The calculator converts frames into seconds automatically.
4. What is the Strouhal number?
The Strouhal number compares tail frequency, tail amplitude, and swimming speed. It is dimensionless. It helps describe swimming motion efficiency and kinematic style.
5. Why should I enter fish length?
Fish length lets the calculator report body lengths per second. This makes comparisons fairer across small and large fish.
6. What amplitude should I measure?
Use peak-to-peak tail tip amplitude. Measure from the farthest left tail tip position to the farthest right position during steady swimming.
7. Can distance be zero?
Yes, for restrained or station-holding observations. Frequency can still be calculated. Swim speed and Strouhal interpretation become limited when distance is zero.
8. Does water temperature affect frequency?
Temperature can affect fish movement and muscle performance. This calculator records temperature as context, but it does not adjust the physics formulas automatically.