Seat belts, airbags and occupant restraint systems

Why it matters

The body structure slows the car; restraints slow the occupant. A three-point seat belt is estimated to roughly halve the risk of death for front-seat occupants in serious crashes, and airbags add protection only when used with belts. Every Indian car now carries dual front airbags and seat-belt reminders, and restraint engineering is where crash mechanics meets human tolerance.

Key ideas

The "second collision". In a crash the vehicle decelerates first. An unrestrained occupant keeps moving at the original speed until striking the steering wheel, dashboard or windscreen — after the car has already used up much of its crush — and then stops over a few centimetres. The aim of restraints is to couple the occupant to the vehicle early so that the occupant rides down the vehicle's deceleration and stops over the longest possible distance with forces spread over strong parts of the body (pelvis, rib cage, shoulder).

Three-point seat belt. A lap belt across the pelvis plus a diagonal belt across the chest and shoulder. Components:

• Emergency locking retractor (ELR): lets the webbing move freely in normal use but locks when it senses vehicle deceleration (pendulum or ball sensor) or rapid webbing pull-out (webbing-sensitive sensor).
• Pretensioner: a pyrotechnic (or electric) device in the retractor, buckle or anchor that fires within roughly 10–20 ms of crash detection and pulls in slack (often around 100 mm or more), coupling the occupant to the car early.
• Load limiter: typically a torsion bar in the retractor that yields at a set belt force (a few kN), paying out webbing so chest load stays below injury levels while the airbag takes over. The energy absorbed is force × payout.
• Anchorages in the B-pillar, sill and seat, designed to regulated strength; adjustable upper anchors fit different occupant sizes.
• Seat-belt reminders with audible and visual warnings, now required for front and increasingly for rear seats.

Airbags (supplemental restraint system, SRS).

• Sensing: accelerometers in the central airbag control unit plus satellite sensors in the front and sides. The algorithm must decide within about 10–20 ms whether the crash is severe enough (roughly above an equivalent rigid-barrier speed of about 20–30 km/h for frontal bags) and not fire in rough-road or minor knocks.
• Inflation: a pyrotechnic or hybrid (stored gas plus pyrotechnic) inflator fills the bag in about 25–40 ms (driver bag roughly 50–70 L, passenger bag roughly 100–150 L). Vents let the bag deflate as the occupant loads it, so it absorbs energy rather than bouncing the occupant back.
• Types: driver and passenger frontal, knee, side (thorax/pelvis) in the seat back, curtain (head protection along the windows; stays inflated longer for rollover), and far-side centre airbags.
• Adaptive features: dual-stage inflators, seat-position and occupant classification sensors (switching off the passenger bag for small occupants or rear-facing child seats), and seat-belt status input.
• Risks: an occupant who is too close (out of position) can be injured by the deploying bag. Hence: always wear the belt, sit at least about 25 cm from the steering-wheel hub, and never place a rear-facing child seat in front of an active passenger airbag.

Side impacts leave very little space, so side and curtain bags must be fully inflated in roughly 10–20 ms.

Child restraints: rear-facing seats for infants, forward-facing seats with harness, then boosters; ISOFIX anchorages give a rigid, correctly installed connection.

Timing logic. A classic rule of thumb: the bag should be fully inflated by the time an unrestrained occupant has moved about 125 mm (5 in) forward relative to the car; subtracting the inflation time gives the latest allowed trigger time.

Formulas

a_occ = V² / (2·(s_v + s_r)) — average occupant deceleration when coupled to the vehicle (m/s²); s_v vehicle crush (m), s_r restraint ride-down distance (belt stretch, chest compliance, airbag stroke) (m).

F = m·a — restraint force on the occupant (N).

x_rel = ½·a_v·t² — forward displacement of a free occupant relative to a vehicle decelerating at a constant a_v (m), valid while the vehicle is still moving.

t_x = √(2x / a_v) — time for the occupant to move x relative to the vehicle (s).

t_trigger = t_125 − t_inflate — latest airbag firing time (s) from the 125 mm rule.

E = F_LL·Δs — energy absorbed by a load limiter of force F_LL (N) paying out Δs (m) of webbing (J).

a = ΔV / Δt — average deceleration over a pulse of duration Δt (m/s²).

Worked examples

Example 1 (standard) — belted vs unbelted. A car hits a rigid barrier at 56 km/h; its front crushes 0.6 m. A 75 kg belted occupant gets 0.3 m of ride-down from the belt and airbag. (a) Find the occupant's average deceleration and restraint force. (b) For comparison, an unbelted occupant strikes a rigid surface after the car has stopped and is brought to rest by 0.05 m of chest compression. Find the deceleration.

1. V = 15.56 m/s; V² = 242.0 m²/s².
2. (a) a_occ = V²/(2(s_v + s_r)) = 242.0/(2 × 0.9) = 134 m/s² (13.7 g); F = 75 × 134.4 = 10.1 kN, spread over pelvis and chest.
3. (b) a = 242.0/(2 × 0.05) = 2420 m/s² (about 247 g) — far beyond human tolerance. The belt turns an unsurvivable impact into a survivable one by using the car's crush distance.

Example 2 (GATE level) — airbag firing time. The same car decelerates at an approximately constant 186 m/s² (19 g) over its 0.65 m crush (crash duration 84 ms). The passenger airbag needs 30 ms to inflate fully. Using the 125 mm rule, find the latest trigger time. Also find when an occupant who is effectively unrestrained would have moved 0.3 m.

1. t_125 = √(2 × 0.125/186.1) = √(0.001343) = 36.6 ms.
2. t_trigger = t_125 − t_inflate = 36.6 − 30 = 6.6 ms after first contact — the sensing algorithm must decide extremely early in a severe crash.
3. t_0.3 = √(2 × 0.3/186.1) = 56.8 ms — still before the car stops (84 ms), so the occupant meets the interior while the car is decelerating.
4. With a pretensioner firing at about 10 ms, belt slack is removed and the relative motion is much smaller, which is why belts and airbags are designed as one system.

Common mistakes

• Treating the airbag as a substitute for the belt. Airbags are supplemental; unbelted occupants can be injured by them.
• Using the vehicle's deceleration as the occupant's: the occupant's peak is higher, and lower only if restraints couple early.
• Assuming crash durations of seconds. Frontal crash pulses last about 70–120 ms.
• Confusing pretensioner (removes slack early) and load limiter (limits peak belt force by paying out).
• Placing a rear-facing child seat in front of an active airbag.

For GATE ME

Expect kinematics and work–energy problems: occupant deceleration over combined crush and ride-down distance, restraint force, airbag timing with relative motion, energy absorbed by a load limiter; plus conceptual questions on ELR, pretensioners, load limiters, airbag sensing and types.

Quick check

1. A load limiter set at 4 kN pays out 150 mm. Energy absorbed?
2. What does a pretensioner do, and when?
3. Car decelerates at 200 m/s². How long until a free occupant moves 0.1 m relative to it?
4. Why do curtain airbags stay inflated longer than frontal bags?

Answers: 1. 600 J. 2. Pulls in belt slack within about 10–20 ms of crash detection. 3. √(2 × 0.1/200) ≈ 31.6 ms. 4. To protect heads during rollovers, which last much longer than a frontal crash.