Sine Sweep Calculator: Crossovers & Sweep Time

List the levels of a sine sweep in order, each as a displacement, velocity or g. The table finds the crossover frequency where each level hands over to the next. You get the sweep time and cycles, the peak values at every corner, and a check against your shaker's stroke, velocity and force.

Sweep profile

Profile

Start from

Standard: log sweep at 0.221 oct/min or slower, 3 h per axis.

Start, Hz End, Hz

Enter as

Sine sweep levels in order. Each row ends at the crossover with the next level unless you type a frequency.
#	Level	Unit	Ends at Hz
1	0.2	in DA (pk-pk)	13.99
2	2	g peak	32.96
3	0.036	in DA (pk-pk)	52.12
4	5	g peak	500

Sine sweep breakpoints: frequency and amplitude, joined by straight lines on log-log axes.
#	Frequency Hz	Amplitude	Slope dB/oct	Delete point

typed calculated

Keyboard and paste

Tab moves level → unit → ends at, then to the next row. Tab from the last row's unit adds a level.
Enter, ↓ and ↑ move down and up the same column.
"Ends at" fills in with the crossover to the next level (grey italic). Type a frequency to make the level step there instead. Clear it to go back to the crossover.
Two levels of the same quantity in a row (1 g then 2 g) never cross, so the first needs a frequency.
Ctrl+Delete removes the current row. Esc undoes the cell you are in.
Paste lines such as 0.20 in DA, 2 g, 5 mm or 10 in/s into a level cell.
Breakpoints (any shape) takes a curve given as frequency and amplitude pairs, such as ISO 16750-3 Table 2. The points are joined by straight lines on log-log axes, the way a vibration controller draws them. Paste two columns (Hz, amplitude) into any cell. Switching from levels fills the points from the current profile's corners.

Sweep rate and time

Sweep Rate, oct/min One sweep, min Sweeps

Enter the rate or the time for one sweep; the other fills in. A sweep is one pass, up or down.

Total3 h

6 sweeps of 30 min, 0.2215 oct/min (6.644 octaves). 1,160,869 cycles in all.

Hz	Level	Time per sweep	Cycles per sweep
5–13.99	0.2 in DA	6.7 min	3,512
13.99–32.96	2 g	5.59 min	7,418
32.96–52.12	0.036 in DA	2.98 min	7,488
52.12–500	5 g	14.7 min	175,060

Opens the sine vs random page with this profile. It is passed in your browser's storage, not sent anywhere.

Values at each corner

Every segment is a straight line on log-log axes, so the largest displacement, velocity and g always fall on a corner. The largest of each is highlighted.

Frequency, Hz	Acceleration, peak	Velocity, peak	Displacement, pk-pk
5	0.256 g2.51 m/s²	3.14 in/s79.8 mm/s	0.200 in5.08 mm
13.99	2.00 g19.6 m/s²	8.79 in/s223 mm/s	0.200 in5.08 mm
32.96	2.00 g19.6 m/s²	3.73 in/s94.7 mm/s	0.0360 in0.914 mm
52.12	5.00 g49.0 m/s²	5.89 in/s150 mm/s	0.0360 in0.914 mm
500	5.00 g49.0 m/s²	0.614 in/s15.6 mm/s	3.91×10⁻⁴ in0.00994 mm

Standard sine profiles, checked

Every profile in the "Start from" list is built from the levels its standard gives. The table finds the corners as crossovers; this table compares them with the corners the standard prints.

Standard, curve	Levels	Range, Hz	Corners printed, Hz	Corners here, Hz
MIL-STD-810H Fig. 514.8E-2	0.20 in DA, 2 g, 0.036 in DA, 5 g	5–500	14, 33, 52.1	13.99, 32.96, 52.12
DO-160G Fig. 8-2, curve Y	0.1 in DA, 1 g, 0.036 in DA, 3 g	5–2000	14, 24, 40	13.99, 23.31, 40.37
DO-160G Fig. 8-2, curve Z	0.1 in DA, 1 g, 0.036 in DA, 10 g	5–2000	14, 24, 74	13.99, 23.31, 73.71
DO-160G Fig. 8-2, curve W	0.1 in DA, 1 g, 0.036 in DA, 10 g, 0.01 in DA, 20 g	5–2000	14, 24, 74, 141, 200	13.99, 23.31, 73.71, 139.9, 197.8
DO-160G Fig. 8-3, curve M	0.1 in DA to 15 Hz, 0.01 in DA, 1.5 g	5–500	15, 55	15, 54.17
DO-160G Fig. 8-3, curve L	0.1 in DA to 15 Hz, 0.02 in DA, 3 g	5–150	15, 55	15, 54.17
DO-160G Fig. 8-3, curve T	0.1 in DA to 15 Hz, 0.036 in DA, 10 g	5–500	15, 74	15, 73.71
DO-160G Fig. 8-3, curve U	0.1 in DA, 20 g	5–150	62	62.55
ISO 16750-3 Test I, curve 1	Breakpoints 100, 200, 240, 270, 440 Hz at 100, 200, 200, 100, 100 m/s²	100–440	200, 240, 270	200, 240, 270
ISO 16750-3 Test I, combined	Breakpoints 100, 150, 200, 240, 255, 440 Hz at 100, 150, 200, 200, 150, 150 m/s²	100–440	150, 200, 240, 255	150, 200, 240, 255
ISO 16750-3 Test I, curve 2	159 mm/s peak, 150 m/s² peak	100–440	150	150
ISO 16750-3 Test VI	0.72 mm peak, 120 m/s² to 260 Hz, 90 m/s² to 350 Hz, 60 m/s²	20–520	65, 260, 350	64.97, 260, 350

DO-160G draws its Figure 8-2 and 8-3 curves on log-log axes and labels the corners rounded: the 1 g to 0.036 in DA corner is labelled 24 Hz, but the two levels cross at 23.3 Hz. The calculator uses the exact crossover. The end frequencies of the Figure 8-2 and 8-3 curves are read from the figures. DO-160G sweeps at 1 octave per minute or slower: one hour minimum per axis for the standard test (8.5.1), three hours including resonance dwells for the robust test (8.7.1). Table 8-1 says which curve applies to each aircraft type and zone.

ISO 16750-3 gives sine levels as amplitude (peak) of acceleration in m/s², and Test VI's low end as 0.72 mm displacement amplitude (peak, 1.44 mm pk-pk). Test I curve 1 and the combined curve have segments that slope at neither constant displacement, velocity nor acceleration (200 m/s² at 240 Hz falling to 100 m/s² at 270 Hz). They open in breakpoint mode with the points of Table 2, joined by straight log-log lines.

Shaker check

Can the shaker run it? Units

Stroke, in pk-pk Velocity, in/s peak Sine force, lbf peak Moving mass, lb

The values filled in are an example, not a real shaker. Enter your shaker's ratings. Moving mass is the armature, the fixture (or slip table) and the test item together. Leave a field blank to skip that check.

	Profile needs	Shaker limit	Used
Displacement	0.200 in pk-pkat 5 Hz	1.00 in pk-pk	20%
Velocity	8.79 in/sat 13.99 Hz	60.0 in/s	15%
Acceleration	5.00 gat 52.12 Hz	25.0 g	20%

Profile chart

Acceleration vs frequency

The dashed red line is the shaker limit: the smallest of its stroke, velocity and force limits at each frequency. The profile must stay below it everywhere.

Reference Guide: Sine Sweep Profiles

Reading a Sine Sweep Profile

Levels and crossovers

A sweep profile holds one quantity constant in each band: displacement at low frequency, sometimes velocity in the middle, and g at high frequency. Where one level hands over to the next, both give the same motion. That frequency is the crossover.

Specs often print only the levels and the overall range. MIL-STD-810H Figure 514.8E-2 prints its corners too: 0.20 in DA to 14 Hz, 2 g to 33 Hz, 0.036 in DA to 52.1 Hz, then 5 g to 500 Hz. The table above computes 13.99, 32.96 and 52.12 Hz from the levels alone.

Crossover formulas

g and DA (inches): f = √(g / (0.0511 · DA))
g and peak velocity (in/s): f = 386.09 · g / (2π · v)
velocity and DA: f = v / (π · DA)

A step in the same quantity (1 g to 2 g) has no crossover. Type the frequency where it steps in the "Ends at" column.

Sweep Rate, Time and Cycles

Logarithmic sweep

Frequency doubles at a steady rate, given in octaves per minute. The number of octaves is log₂(f₂/f₁), so

time = log₂(f₂/f₁) / rate.

5 to 500 Hz is 6.644 octaves. At 1 oct/min that is 6.64 minutes; in 30 minutes it is 0.2215 oct/min.

Cycles in one sweep: N = (f₂ − f₁) / (R · ln 2), with R in octaves per second.

Linear sweep

Frequency rises a fixed number of hertz per second: time = (f₂ − f₁) / rate and N = (f₂² − f₁²) / (2 · rate).

A log sweep spends the same time in every octave, so each resonance gets about the same number of cycles in its half-power band: fₙ / (Q · R · ln 2). A linear sweep rushes through the low octaves and lingers at the top.

Shaker Limits

Three limits

Stroke (peak to peak travel) limits the low frequencies. Velocity limits the middle. Force limits the high frequencies: the g the shaker can reach is its rated sine force divided by the total moving mass.

Moving mass includes the armature, the fixture or slip table, and the test item. A heavy fixture can take most of the shaker's force.

Margins

The check above compares the largest corner value of each quantity with the rating. Over 80% is shown amber, over 100% red.

This is a first check only. Resonances of the fixture and test item can raise the force the shaker needs well above mass × g. Use the manufacturer's performance curves for the final check.

Sources

MIL-STD-810H, Environmental Engineering Considerations and Laboratory Tests, Method 514.8 Vibration (31 January 2019; public release). Annex E, Figure 514.8E-2 (Category 24, helicopter minimum integrity exposure: 5–500 Hz, 30 minute logarithmic sweep, maximum three hours per axis).

RTCA DO-160G (2010), Section 8 Vibration: Figures 8-2 and 8-3 (sine test curves), Table 8-1, paragraphs 8.5.1 and 8.7.1 (sweep rate and test time).

ISO 16750-3:2012, 4.1.2.1 (Test I, Table 2, all three curves) and 4.1.2.6 (Test VI, Table 9): sine levels, sweep rate of 0.5 octave/minute or less, and test times.

Standard gravity g = 9.80665 m/s² (exact, CGPM 1901); 1 in = 25.4 mm and 1 lbf = 4.4482216152605 N (exact).

The crossover, sweep time and cycle formulas are derived on this page from simple harmonic motion and the sweep law. The tests in this site's code check them against the corners MIL-STD-810H prints for Figure 514.8E-2.

Sine Sweep Profile Calculator: Crossover Frequencies, Sweep Rate and Time, Cycles, and Shaker Stroke, Velocity and Force Check