The physics of Thunderbird 3

Theo de Klerk

The third countdown on physics of the International Rescue craft concerns the spaceship Thunderbird 3. The tallest and fastest of all Thunderbirds it doesn't get as much play time in the adventures as it should have gotten. It is the only Thunderbird that is piloted by most of the Tracy brothers (in Ricochet by Virgil and Brains) but usually either Alan or John is at the helm, assisted by eldest brother Scott. The spaceship looks like any rocket and is quite believable in design. There are some observations however that could do with some improvement.

Thunderbird 3 reverse plan
Reverse Plan
Thunderbird 3 plan
Plan
Thunderbird 3 front
Front elevation
Thunderbird 3 rear
Rear elevation

Updated technical specifications [changes are set in bold italic font]

Shape

Because Thunderbird 3 rushes through a dense Earth atmosphere as well as the vacuum of space, the living compartments of the Thunderbird 3 astronauts are pressurized compartments.

Rockets have an easier time in space than submarines under water. For the latter, every 10 metres deeper down results in additional layers of water above that cause an extra pressure of 1 atmosphere. Rockets in space travel through a constant near vacuum and the pressure difference between deep space and the pressurized interior of the living quarters remains around 1 atmosphere.

Thunderbird 3 mostly adheres to a streamlined, bullet shaped vessel allowing air to pass along its hull while speeding from launch bay to the vacuum of space at supersonic speed. Protruding parts that cause friction are the white docking ring and the top of the nacelle rockets. Both are rather blunt in shape — a more smooth aerodynamic shape allows the air to flow past more easily without bumping on the surfaces causing drag. Supersonic speed problems will be discussed at length when we look at Thunderbirds 1 and 2.

Once in space, the shape of Thunderbird 3 has little or no bearing on its functioning or speed to travel.

Launch

Thunderbird 3 launch Thunderbird 3 launch
(The Uninvited launch 20:56 to 20:59 minutes — stock footage)
graph
acceleration up to lunar orbit
graph
up to lunar orbit by time

Watching Thunderbird 3 take off stock footage in The Uninvited and taking scale factors into account, it seems to raise itself 9.3 metres within the first three seconds after launch, equating to an acceleration of about 2.1m/s2 upwards. This is on top of the compensation for the downward Earth gravitational pull (9.8m/s2 — better known as '1g'). Therefore, Thunderbird 3's thruster nacelles produce an acceleration of 9.8 + 2.1 = 11.9m/s2 (1.2g). Any value above 1g is sufficient to leave the Earth. To accomplish this, the three nacelles each produce a force of over 220kN. This seems a rather low value to rush into space quickly. Even the old Saturn V rocket that propelled Apollo capsules into orbit had an initial thrust of 34,000kN which is more in line with the technical specification (written well before the Saturn V launches) for Thunderbird 3 that claim a thrust of about 20,000kN. This thrust would equal an acceleration of Thunderbird 3 of 35m/s2 (3.5g) and does require astronauts to be strapped in and lying flat instead of sitting in a chair the way Scott and Alan are shown to do.

You can model the movement of Thunderbird 3 given its acceleration and the knowledge that its thrust is less and less opposed by the gravitational pull of Earth at greater distances from the planet. The first graph shows both suggested accelerations of 1.2g (thrust 1) or the more likely 3.5g (thrust 2) during travel to a distance of the lunar orbit.

It is clear that the higher thrust needs less time to cover this distance and has a higher acceleration. At around 143 thousand kilometres the braking influence of Earth can be ignored.

The second graph below shows the distance from Earth in relation to the time travelled. The distance is limited to the lunar orbit, assuming most rescues happen within this range.

Some relevant travel data at the acceleration of 3.5g is summarized in the table below. The altitude is measured from the Earth's surface. For calculations the radius of the Earth (6371km) must be added, though beyond the Thunderbird 5 orbit it becomes insignificant for the results.

target altitude travel time 1.2g travel time 3.5g
Earth – exosphere 1,000 km 15 minutes 5 minutes
Earth – Thunderbird 5 95,500 km 84 minutes 41 minutes
Earth – Moon 384,400 km 2.5 hours 80 minutes
Earth – Sun 150,000,000 km 1.9 days 1.1 days

Some important data for most of Thunderbird 3's rescues shown in the series is summarized in the table below.

Thunderbird 3 missions altitude travel time 1.2g travel time 3.5g
Low Earth Orbit (LEO) (Alpha-2-0 in Cry Wolf, Space Observatory 3 in Impostors, KL-A in Ricochet) 300-600 km 12 minutes 3 minutes
geostationary orbits 36,000 km 60 minutes 27 minutes
Sun Probe (vicinity of the Sun) less than 150,000,000km less than 1.9 days less than 1.1 days

Thunderbird 3 is a lot more fuel efficient than the Saturn V rockets that brought the Apollo capsule in an orbit around the Earth. According to NASA figures, the Saturn V requires 1,675,000 litres of fuel to reach a 67 km high orbit and in doing so loses all of the three rocket stages. Thunderbird 3 remains complete and exceeds Saturn V in all reusability aspects as well as fuel efficiency.

Re-entry

It is not shown often how Thunderbird 3 makes its re-entry in the Earth's atmosphere at the completion of a rescue or visit to Thunderbird 5. Only the final stage where its rockets fire and the space ship makes a slow descent into the round house is shown. It is assumed it will land precisely on the three rocket cradles in the launch bay.

In principle, re-entry is nothing else than launch in reverse. At launch it tries to get to the rescue zone as quick as it can. It is full thrust upwards in competition with the gravitational pullback.

On re-entry there is no haste to get back. A different approach can be taken. Isaac Newton's law applies: an object moves with a constant speed if there is no net force working on it. So if Thunderbird 3 can slow down to a slow descent rate and then uses its rockets only to compensate upwards for Earth's pull downwards, it will descend at a fixed speed. With no thruster rockets, it would simply plunge down and reach the ground with a deadly speed of 11.2km/s (the escape velocity of Earth).

Thunderbird 3 landing Thunderbird 3 landing Thunderbird 3 landing Thunderbird 3 landing Thunderbird 3 landing Thunderbird 3 landing

To allow the Thunderbird 3 rockets to work, all its astronauts have to do is to turn the space ship around in such a way that its tail is pointing to Earth — just as it would be positioned during launch escaping from Earth. This way the rockets can be ignited and lower the spaceship gently into its hangar. The increasing air friction in the lower atmosphere also slows down the space ship so the rockets need only compensate for the gravitational pull as far as the air friction does not.

The air friction does cause another problem: it heats up all surfaces that try to move through the air. For our spaceship this is mostly the blue underbelly of Thunderbird 3 and its nacelle thrusters. These must be very heat resistant or cooled. The rear side of Thunderbird 3 is blunt rather than pointed. Since the spaceship can control the rate of descent, the air friction need not become very high. Although the air may become ionized, blocking communication, this is mostly at the bottom, allowing communication with Thunderbird 5 to remain available.

When the Round House comes into sight, Thunderbird 3 needs to slow down much more, implying its rockets must actually break its speed and produce a higher force than needed to only compensate for gravity. At the final slow descent it can manœuvre itself through the Round House and into its three rocket cradles. No doubt computer guidance is used between sensors and computers inside the Round House and the guiding system of Thunderbird 3 itself. This is an automated procedure as the astronauts have little view on what's happening at the tail end of the rocket and would be too slow to respond on meter readings.

Space travel

For its launch, Thunderbird 3 must accelerate from standstill to at least escape velocity. But once this is surpassed the astronauts of Thunderbird 3 may decide to switch off the engines. The speed obtained will be kept almost indefinitely according to Newton's First Law provided no opposing force it working on it (like solar wind). The spaceship can glide to its destination without any fuel consumption.

Manoeuvring in space: rotation and attitude

Thunderbird 3 will normally move in a forward direction. For precise sideways manœuvring in space Thunderbird 3 uses small pitch and yaw rockets positioned around the rocket. A small blast from one or more of these and the spaceship will change its course or position. This is essential during docking procedures with Thunderbird 5.

Thunderbird 3 must reduce its speed relative to Thunderbird 5 to almost nil and then make adjustments to align and dock with the space monitor. The episodes are accurate not to show any blasts from the main rockets in the process.

Another, much more economical way allowing for much more precise changes than the yaw rockets is the flywheel (or reaction wheel) inside the rocket. Flywheels are often used in space ship: the Hubble telescope uses it to keep it focused on one particular star, which requires very minute adjustments to its attitude.

Artificial Gravity

The thrust of Thunderbird 3's rockets produces an artificial gravity in a similar way that one feels heavier when an elevator starts to move upwards. While traveling with a 3.5g acceleration, everything aboard will weight 3.5 times as much as on Earth. At constant speed there is no acceleration and everything becomes weightless and floats around if not strapped tight. It's important to realize that 'airless' does not imply 'weightless'.

On arrival at the rescue scene, Thunderbird 3 must put on the brakes (fire counteracting rockets) and come to a standstill in relation to the satellites or rockets in trouble. The situation is comparable to standing in a train carriage that abruptly slows down: one 'moves on' and feels as if one is thrown forward through the carriage. The astronauts, as well as all loose objects, are thrown forward as if the ceiling suddenly becomes the floor.

Engine types

Every object moves because it pushes on something (be it the road or an exhaust gas) and this something pushes back with the same force. This is known as Newton's Third Law. It has baffled many people but it is the essence of any object traveling through space. Throwing out engine exhaust gas in a backward direction, results in an equal force forward on Thunderbird 3. Only the speed and amount of gas expelled each second determines the forward thrust. Lots of cold water or coffee beans expelled from the engine can give the same result as hot kerosene. But the latter is far easier to use to get the thrust needed.

Thunderbird 3 needs to reach escape velocity (11.2km/s) and beyond to get into deep space. For rescues 'fast' by high acceleration and thrust is the keyword. Currently this can only be achieved using chemical rockets that burn fuel and in doing so release large amounts of energy to build the thrust. It is an inefficient process in that it requires an enormous bulk of fuel to be burned. Judging by the amount of chemical fuel Thunderbird 3 needs, it seems difficult to locate sufficient room inside the space ship to accommodate this fuel. It's a problem with all Thunderbirds machines: it remains a mystery where the fuel is stored in each of them.

An alternative source of thrust is said to be the ion drive or ion propulsion. It sounds futuristic, but won't work for high thrusts. Ions are atomic nuclei – with minute masses of 10—24kg as opposed to chemical fuel of typically 104kg – a factor change of 1028. The charged ions achieve a high acceleration when passing through a properly oriented electric field. However, their mass is so minute that the thrust force each ion obtains is also minute and hence they hardly accelerate Thunderbird 3 with its huge mass. Ion propulsion is used in satellites that go beyond the solar system but they are in no hurry to get there. For Thunderbird 3 time is of paramount importance and ion drives are not useful here. The small acceleration would also never exceed that of Earth's gravitational pull and using ion drive the spaceship would never leave its hangar as it never exceeds Earth's downwards gravitational pull.

The location of the ion rockets in Thunderbird 3 is correct had they been used: the three side arms would provide the distance needed for the ions to be accelerated by an electric field. Inside the main chemical rocket outlets electrons would recombine with the speeding ions to become speeding uncharged atoms that leave Thunderbird 3 through the rocket outlets.

Engine positioning

To have three thrusters in the three nacelles is not the most stable of configurations. The centre of gravity of the rocket obviously lies somewhere along the central axis connecting head and tail of the rocket. The three rockets are positioned symmetrically around it and when all give the same thrust, Thunderbird 3 will speed straight forward. If one of the rockets gives a slightly bigger or smaller thrust than the other two, the rocket will have a net force outside the central axis, causing it to move along a curved trajectory. This is definitely the case if one of the rockets fails.

Look at the figure above where only one engine works. It provides an upward thrust on one side of the space ship. The line along which this thrust force works is not through the centre of mass of Thunderbird 3. Because the line of force is at a distance from the centre of mass, this distance works as a lever by which the force starts to tilt the rocket and move it sideways (to the right). The rocket starts to move in a circular orbit.

To avoid this imbalance of thurst, a more symmetric set of thrust rockets is preferable. When each of the three rockets is paired with another one on the other side of the rocket, a more stable configuration is obtained. This would look more like the Russian Vostok and Sojuz rockets — even Sun Probe. When one rocket fails, Alan can switch off the opposite rocket too to maintain a straight course. The remaining rockets provide a balanced forward thrust on all sides of the space ship. Having a double set of engines, the thrust can also double from 3.5g to 7.0g total. This makes the space ship faster (but Alan would feel like weighing 7 times as much as on Earth.

A whole circular arranged set of rockets would be even more stable, given that there cannot be a main thruster rocket in the middle since the sofa with the astronauts boards the ship that way.

Launch and travel position

maximum G forces for an astronaut
Direction of maximum allowable force (acceleration) for astronauts

The human body can only endure accelerated motions to some extent — partly dependent on the human shape. The acceptance levels Alan Tracy and his co-pilots of Thunderbird 3 can endure in different directions of movement are illustrated below. If the spaceship moves upwards, the gravity felt is downwards. At 15 times Earth gravity (15g) an astronaut lying flat will pass out and die.

It is certainly a good idea to lie down as Alan does in Thunderbirds are GO! and the second series. Piloting Thunderbird 3 standing up or sitting normally as suggested in the first series is not a very good idea: at 5g acceleration he would pass out. When traveling at emergency thrust of 10g or sustainable thrust at 6g, as suggested by some publications, the astronauts must lie down if they want to survive the acceleration.

Once Thunderbird 3 has reached a cruising speed and stops accelerating, the engines are shut off and the speed stabilizes to a constant value. The fact that Thunderbird 3 is seen to speed through space without any of its rockets blasting, is therefore pretty accurate. Traveling at constant speed does imply that everything (including the astronauts) becomes weightless and starts floating about. This is not shown in the episodes. It remains a miracle that the books behind Scott will stay put. One wonders why there are bookshelves in Thunderbird 3 in the first place.

Sitting down is not good practice launching a rocket

Radio beam

To rescue the Sun Probe rocket, a radio beam was used to activate the remote control mechanism of Sun Probe. Assuming the Sun Probe was in the vicinity of the Sun (say 10,000,000km from it) and that radio beams travel with the speed of light, we can calculate how far Thunderbird 3 was removed from Sun Probe. The tractor beam, overrun by .5 in power (why not use maximum power immediately?), took a dramatic 19 seconds traveling at light speed to reach Sun Probe and return a signal to Thunderbird 3, implying it was 9.5 light seconds or 2,350,000km away from Thunderbird 3. That means Thunderbird 3 travelled a distance of about 137,650,000km from Earth. According to earlier calculation models this must have been around 1.1 days after launch from Tracy Island at normal 3.5g thrust. If they used the maximum sustained acceleration of 6g it would take only around 18 hours, provided Scott, Alan and Tin Tin were strapped in flat.

With the knowledge gained, the initial cutaway released on Thunderbird 3 needs some updating (text in bold italic font).

Thunderbird 3 cutaway drawing Thunderbird 3 dock Thunderbird 3 lounge
Move the pointer over the numbers in the drawings to access the legend
Tap a circle to access the legend – tap anywhere else to cancel
Chemical rocket explosion chamber; chemical rockets are used for take-off and boost and normal rescue flights
Gate seal blocking off particle accelerator from explosion chamber when chemical rockets are firing
Particle accelerator for ion engines – unlikely to be of any use
Particle gun; once escape velocity is reached, the three particle accelerators provide a steady continuous acceleration by means of an exhaust stream of atomic particles – but a minute acceleration Thunderbird 3 cannot use if it needs to perform a rescue; usage unlikely
Radiant cooling fins
Ring of pitch-and-yaw jets
Propellant tanks for main motors, helium pressurised
Ring of atomic electricity generators provide power for particle accelerators and auxiliaries – unlikely to be used for particle accelerators
Shielding protecting entry tunnel through which ramp-operated seat 'loads' crew
Rectifiers
Flywheel rotor assemblage; the spinning flywheel makes the ship turn in the opposite direction of the spin rate
Retro rockets
Retro rockets fuel
Sensors for guiding Thunderbird 3 to lock on position when docking with Thunderbird 5
Additional retro rockets
Entry tunnel, used in flight as an air-reservoir
Lift to upper decks
Ramp-entry chair, centered in the lounge
Bunks – sleeping accommodation
Twin-walled hull at this point for extra meteor protection; All such spare spaces such as this are filled with propellant which is unlikely without pumps to direct it to the rockets where needed – also in constant speed flight when there is no artificial gravity
Essential life-support services (air-recycle pumps, heating, etc.) under the floor
Stores level
Twin-seat pilot position
Flight computers serving console below
Domed bulkhead of inner 'living space' capsule (pressurised)
Sensors, accelerometers and other flight instruments
Forward pitch-and-yaw correction jets
Hangar, Thunderbird 5
Sensors on the ring on Thunderbird 3 guide the nose into the docking port
Electro magnets clamp the ring of Thunderbird 3 to form an airtight seal; air is then pumped into the hangar to correct pressure and a warning light informs the pilot that it is safe to open
Exit hatch
Ramp into the satellite
Airlock door to inspection platform
Ramp entry seat
Air duct
Library of microfilms digital information media queried by remote control and shown on monitor screen K or any tablet
Intercom speaker
Monitor screen
Lift to other floors
References:
Spacecraft Systems and Engineering 3rd Ed – Peter Fortescue a.o. (Editors), John Wiley, 2005
Fundamentals of Astrodynamics – Roger Bate a.o., Dover Publications 1971
Introduction to Flight 5th Ed – John D. Anderson Jr., McGraw-Hill 2005
Thunderbirds Agent's Technical Manual – Haynes, 2012
Thunderbird Code Rood – Albert Heijn, 1966
Thunderbirds Annual 1966
Physics 9th Edition – Cutnell & Johnson
The World of Star Trek – Lawrence Kraus
text ©2014 Theo de Klerk
article originally appeared in fab #80