Example Data Table
| Method | Inputs (summary) | Key output |
|---|---|---|
| Displacement–Time | y1 = 0 m, y2 = 100 m, t1 = 0 s, t2 = 5 s | v_avg = 20 m/s |
| Kinematics | v0 = 20 m/s, a = −9.81 m/s², t = 2 s | v = 0.38 m/s |
| Projectile | v0 = 30 m/s, θ = 45°, y0 = 0 m, t = 1 s | vy ≈ 11.40 m/s |
| Pressure ω → w | ω = −0.20 Pa/s, ρ = 1.225 kg/m³, g = 9.81 | w ≈ 0.0166 m/s |
Formula Used
- v_avg = Δy / Δt for average vertical velocity between two observations.
- v = v0 + a t for constant vertical acceleration.
- vy(t) = v0 sin(θ) − g t for projectile vertical component.
- w = − ω / (ρ g) converting pressure vertical velocity to height-based velocity.
How to Use This Calculator
- Select a method that matches your measurement setup.
- Choose length and time units for the input fields.
- Enter values carefully, respecting sign conventions.
- Press Calculate to display results above the form.
- Use Download CSV or Download PDF for reporting.
Vertical Velocity in Practice
1. What vertical velocity measures
Vertical velocity describes how fast height changes with time. In SI, it is measured in meters per second. A result of +2 means upward motion at two meters each second, while −2 indicates the same speed downward under your sign convention.
2. Choose a clear sign convention
Most mechanics problems use upward as positive, so gravity is typically entered as g = 9.81 m/s² and free-fall acceleration as a = −9.81 m/s². Atmospheric data often uses ω (Pa/s) where ω > 0 commonly corresponds to downward motion.
3. Average velocity from observations
When you have two height samples, the most robust estimate is the average vertical velocity vavg = Δy/Δt. For example, moving from 0 m to 100 m in 5 s yields vavg = 20 m/s. This method is ideal for GPS, lidar, and lab tracking.
4. Constant-acceleration kinematics
If acceleration is approximately constant, use v = v0 + a t and Δy = v0 t + 0.5 a t². With v0 = 20 m/s, a = −9.81 m/s², and t = 2 s, the calculator returns v ≈ 0.38 m/s and Δy ≈ 20.38 m.
5. Projectile vertical component
For launch problems, the vertical component is v0y = v0 sin(θ). The vertical velocity evolves as vy(t) = v0y − g t. The time to apex is tapex = v0y/g, and the peak height increase is v0y²/(2g).
6. Converting ω to w in meteorology
Vertical motion in pressure coordinates uses ω = dp/dt. Convert it to height-based velocity w using w = −ω/(ρg). With ω = −0.20 Pa/s, ρ = 1.225 kg/m³, and g = 9.81 m/s², you get w ≈ 0.0166 m/s, a modest updraft.
7. Units and scaling sanity checks
Keep a quick scale sense: human elevators are often around 1–3 m/s, strong convective updrafts can exceed 10 m/s, and gentle atmospheric ascent may be below 0.05 m/s. If your result is wildly outside expectations, recheck units and signs.
8. Reporting, uncertainty, and validation
Exporting CSV and PDF helps document assumptions, inputs, and formulas. For measured data, estimate uncertainty by propagating errors in Δy and Δt; small time intervals amplify noise. Validate with a second method when possible, such as comparing Δy/Δt against kinematics over the same window. Include sampling rate and timestamp precision; for example, 10 Hz sampling implies 0.1 s granularity, limiting velocity resolution.
FAQs
1) What does a negative vertical velocity mean?
It means motion is in the negative direction of your chosen axis. If you treat upward as positive, a negative velocity indicates downward motion. If you reverse the convention, the interpretation reverses too.
2) Why are outputs shown in SI units?
SI outputs avoid confusion when mixing input units and formulas. The calculator converts your chosen units internally and reports m, s, and m/s consistently, making exports easier to compare across experiments and datasets.
3) Can I use minutes or hours for time inputs?
Yes. Select the time unit you used for the entered times. The calculator converts to seconds internally, so kinematics and projectile equations remain consistent and comparable with other methods in the results table.
4) What if t2 equals t1 in the displacement method?
The time interval becomes zero, so Δy/Δt is undefined. Enter distinct times or use a longer interval. If measurements are noisy, longer Δt often produces a more stable velocity estimate.
5) How is density computed in the ω to w method?
When enabled, density uses the ideal-gas relation ρ = p/(RdT). Provide pressure in pascals and temperature in °C, which is converted to kelvin internally. This is a dry-air approximation.
6) When is the constant-acceleration model appropriate?
Use it when acceleration is roughly constant over the interval, such as short-duration free-fall or controlled motion. If drag or thrust changes significantly with speed or time, the model may deviate and a data-based Δy/Δt method may be safer.
7) What typical ω values should I expect?
They vary by context and altitude. In synoptic-scale ascent, ω might be around ±0.01 to ±1 Pa/s, while stronger convective events can be larger. Always interpret ω alongside density and g when converting to w.