Acceleration Conversion

G-forces are measured by accelerometers — devices where a proof mass is suspended by springs or piezoelectric elements. When the device accelerates, the mass deflects proportionally. MEMS (micro-electro-mechanical systems) accelerometers are ubiquitous in smartphones, airbags, and game controllers. Triaxial accelerometers measure all three components simultaneously. Centrifuges can be calibrated by multiplying rotation rate squared by radius: a = ω²r.

Sustained g-limits: +4g (chest-to-back) for untrained; +9g for trained pilot with anti-G suit + AGSM (straining maneuver). -2g (negative g) causes redout (blood to head). Brief pulse limits are higher: 40g (50 ms) in roller coasters; 100g in ejection seats; ~250g in vehicle crashes (1 ms). The Stapp Rocket Sled experiments showed survival at 46g (0.2 s). At high g, loss of consciousness occurs as blood drains from brain.

1 Gal = 1 cm/s² = 10 mGal = 10⁻² m/s², named after Galileo. In gravimetry, gravity anomalies are measured in mGal (10⁻⁵ m/s²) or μGal (10⁻⁸ m/s²). Earth's gravity varies by about ±50 mGal globally. The GRACE satellite mission measured gravity changes of ~1 μGal/month due to groundwater and ice sheet changes. Superconducting gravimeters achieve sensitivity of ~1 nGal.

Newton's second law: F = ma. Acceleration equals the net force divided by mass. In a gravitational field, the acceleration is independent of mass (Galileo's discovery, verified to 10⁻¹⁵ precision by MICROSCOPE satellite in 2018 — the weak equivalence principle). This equality of inertial and gravitational mass is the foundation of Einstein's general relativity.

Earth orbits the Sun at v = 29.78 km/s, radius r = 1.496 × 10¹¹ m. Centripetal acceleration a = v²/r = (29780)²/(1.496 × 10¹¹) = 5.93 × 10⁻³ m/s² = 0.000605g. This is exactly equal to the Sun's gravitational acceleration at Earth's distance (GM_sun/r² = 5.93 × 10⁻³ m/s²), as required for circular orbit.

Space Shuttle main engine cutoff: ~3g. Saturn V liftoff: 1.25g (low initial thrust ratio), peaking at ~4g before fuel burnout. SpaceX Falcon 9 crew missions: limited to 4g for crew safety. The Soyuz abort system peaks at 14-17g for 5 seconds. During reentry, Soyuz capsule peak deceleration is ~4g, while the Space Shuttle reached ~1.5g due to its long, shallow reentry profile.

Surface gravity (in g): Mercury 0.38g, Venus 0.905g, Earth 1.00g, Moon 0.165g, Mars 0.378g, Jupiter 2.528g (at cloud tops), Saturn 1.065g, Uranus 0.886g, Neptune 1.137g. A 70 kg person would weigh: Moon 113 N (11.5 kg), Mars 259 N (26.4 kg), Jupiter 1731 N (176 kg). On a neutron star: ~10¹¹g — the entire weight of a human would crush to a particle in microseconds.

Jerk (sometimes called 'jolt') is the rate of change of acceleration: jerk = da/dt (m/s³). High jerk is uncomfortable and can cause injury — elevator designers limit jerk to ~2 m/s³; rollercoasters to ~10 m/s³. Snap (4th derivative of position), crackle (5th), and pop (6th) also exist mathematically. In vehicle dynamics, jerk is an important design constraint for passenger comfort.

The Coriolis acceleration is a fictitious acceleration appearing in rotating reference frames: a_Cor = -2Ω × v, where Ω is the Earth's rotation vector and v is the velocity relative to Earth's surface. Its magnitude is about 0.1 mm/s² for typical wind speeds, deflecting winds to the right in the Northern Hemisphere and left in the Southern Hemisphere. This drives the rotation of cyclones and ocean gyres.