a v
c= R2= 102= m s−2 5 00 20 0
. .
Vertical g-force =av+ = + =
g 1
9 80 1 3 04
. .
+20.0
One effect of g-force is that the apparently increased weight of the blood drains it from the head, affecting vision and consciousness. On average, 4 –5 g causes dimming of vision, 5–6 g visual blackout and above 6 g you experience loss of consciousness (‘g-LOC’). Much larger g-forces can be tolerated for periods of less than about 4 seconds.
To increase g-force tolerance during launch, astronauts face the direction of acceleration. This orientation is called ‘eyeballs in’, because the eyeballs are effectively pushed into their sockets. Also, the seats are oriented with the head and body lying horizontally (Figure 2.1.11). In this way, g-force doesn’t easily force blood into or out of the head. Fighter pilots and astronauts also wear
‘g-suits’ containing inflatable bladders in the trousers which squeeze blood out of the legs and back into the head.
Using a powerful cannon to launch a satellite (see Newton’s thought experiment in section 2.2) would not work because of the enormous g-force from the initial explosion.
Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth.
ThE FIRsT asTRoNauTs?
A
ccording to Chinese legend, in 1500 a senior bureaucrat (a Mandarin) called Wan Hu tried to launch himself into space by tying 47 gunpowder rockets to a chair. He failed to become the first astronaut by dying in the explosion at launch.In about 1806 in France, Claude Ruggieri launched a rocket containing a sheep
~300 m into the air, parachuting it back to Earth alive. The police prevented him from turning a small boy into the first astronaut by the same method.
Figure 2.1.11 Gemini 3 astronauts Gus Grissom and John Young strapped into their horizontally oriented seats are being prepared for launch (1965).
Warning! The terms g-force and g-load are not SI quantities. They are informal terms and are sometimes used carelessly. Sometimes g-force and g-load are used to mean the same thing. Sometimes g-load is used to mean only the net acceleration in units of g, not including the effect of gravity. When reading g-force or g-load data, be careful to check which definition is being used.
Force during take-off
Here we’ll account for the forces, accelerations and g-force experienced during a typical launch. This example is for a Space Shuttle, but the principles apply to other craft. In the Shuttle, the solid rockets boosters and the main liquid-propelled engines fire-up at the same time, while in a more traditional multi-stage rocket each multi-stage fires sequentially.
Figure 2.1.12 is a graph of g-force experienced by everything within the Shuttle during launch. Just before lift-off (or take-off), the vector sum of thrust plus the force exerted by the gantry (the crane-like structure holding the rocket) plus the rocket’s weight is zero, so there is no acceleration. Because acceleration is zero, the net force on the astronaut is also zero, so the astronaut’s weight is balanced by the normal force exerted by the seat: g-force = 1 (point A).
After lift-off, thrust is larger in magnitude than rocket weight plus air resistance, so the rocket (and astronaut) accelerate upwards. Now the seat exerts a normal force greater than the astronaut’s weight. The g-force is greater than 1, increasing steadily, along with acceleration as the mass of remaining propellant decreases. Note that throughout the launch process, the craft is ‘pitching over’
from vertical to horizontal motion, so the gravitational contribution to g-force is becoming progressively smaller in the direction of motion.
The ~0.2 drop in g-force between points A and B is due to ‘throttle down’;
air resistance-induced pressure on the Shuttle surface reaches a dangerous maximum (‘max Q’), so thrust is deliberately reduced until the atmosphere thins out. Thrust is increased again and g-force increases to between 2 and 3 (point B).
As the mass of remaining propellant decreases, acceleration (and g-force) increases until fuel in the boosters (or lower stage in a traditional rocket) runs out. Acceleration decreases dramatically, but the boosters (or empty stages) are discarded (point C), and the remaining engines provide the thrust. Acceleration increases again as propellant mass decreases. To avoid the astronauts and payload
Analyse the changing acceleration of a rocket during launch in terms of the:
• Law of Conservation of Momentum
• forces experienced by astronauts.
being subjected to a dangerously high g-force, the thrust must be reduced to limit g-force to 3 g (point D).
Once the rocket is in orbit, the rockets stop firing (point E). The only force acting now is weight (providing the centripetal force of orbit), so the rocket and the astronaut are both in free-fall and effectively weightless; the astronaut experiences a zero g-force.
Running start
It takes a lot of fuel to get a spacecraft to a high enough altitude and high enough speed to achieve orbit. You can get higher if (like a pole vaulter) you get a ‘run-up’ before lift-off. Given that Earth rotates rapidly, a rocket already has a large easterly tangential velocity at launch. So, if you launch towards the east, you can use less propellant, carry a larger payload or go into a higher orbit. The closer you are to the equator, the faster your initial speed u (Figure 2.1.13).
At the equator u = 465 m s–1.
Worked example QUESTIon
Compare Earth’s rotational tangential speed vT at the rocket launch facilities at Woomera, Australia (used during the 60s and 70s), and Kourou, French Guiana.
Data: Earth’s radius rE = 6.37 × 106 m Earth’s rotational period T = 86 164 s
Woomera: Latitude 31.1°S, longitude 136.8°E.
Kourou: Latitude 5.2° N, longitude 52.8°W SoLUTIon
Tangential speed: v R
T=2Tπ (See in2 Physics @ Preliminary p 29.) Radius of rotation R depends on θlat, the latitude angle: R = rEcosθlat Analyse the forces involved in
uniform circular motion for a range of objects, including satellites orbiting the Earth.
Discuss the effect of the Earth’s orbital motion and its rotational motion on the launch of a rocket.
0 100 200 300 400 500 600
3.5 3.0 2.5 2.0 1.5 1.0 0.5
E in orbit D accelerating up
to orbital speed C solid rocket
booster separation
B reduced air resistance
A lift-off
A B
C
D
E Time (s)
g-force
Figure 2.1.12 g-force during a typical Shuttle launch
Earth’s rotation
v1
v2 tangential velocity
Figure 2.1.13 Rockets are usually launched towards the east, to take advantage of Earth’s rotation.
The effect is greatest at the equator.
v r
T TE
lat lat 465
=2 =2 ×6 37 10× =
86164
π cosθ π . 6cosθ cosθllat
Woomera: 465cos31.1° = 398 m s–1 Kourou: 465cos5.2° = 463 m s–1
To explore the solar system, you need to reach Earth’s escape velocity. As the Earth also orbits the Sun, you can get an extra boost from Earth’s orbital speed (about 3.0 × 104 m s–1) if you launch at a time of the year when the Earth’s orbital motion points in the desired direction (Figure 2.1.14).