Complete science reading
The area is impulse
The signed area under a force–time curve equals the impulse. A rectangular constant-force pulse at −30 N lasting 0.40 s gives −12 N·s. For a symmetric triangular pulse that rises linearly from zero to a peak and then returns to zero during that same interval, the area is half the peak times duration.
Same impulse, different peaks
To deliver a prescribed −12 N·s over 0.4 s, a rectangular pulse must have constant −30 N. A triangular pulse of the same signed area and duration needs peak −60 N. Both have mean force −30 N, but the triangle's peak magnitude is twice the rectangle's constant magnitude. The time-integrated force—not the graphical peak alone—determines Δp.
Compare duration and shape independently
With the impulse held at −12 N·s and duration increased from 0.20 s to 0.60 s, the mean magnitude falls from 60 N to 20 N. Pulse shape changes the peak: for our simple symmetric triangle, peak = 2×mean; for the rectangle, peak = mean. The rectangle and triangle are specified ideal shapes, not measured airbags, helmets or padding.
What a model does not predict
Graph area fixes impulse, but knowing impulse and duration alone does not reveal the real peak force. Real-world force curves may be irregular, include repeated impacts, distributed loads and multiple directions. The Force–Time Pulse Studio uses explicit rectangular and triangular assumptions so peaks are mathematical outputs, not safety ratings.