Federation shields are weird things, blocking some but not other things; often, one can bypass shields just by getting right frequency. According to display shown below, shields are composed from gravitons - that explains how they stop particle and projectile weapons - but also must have EM/electronic component. Shields seem to operate on same principles like forcefields that we see on starships, blocking corridors in case of emergency etc.
Shield percentage
When shields are hit by weapons, shield strength falls, and that is expressed in percentages. Here we have another proof that shields use some kind of particles that are knocked out by successive hits, since not only that shields degrade by same/similar percentage with every hit, but also do not seem to be blocking entire quantity of energy directed on ship; efficiency seems to be degrading with successive hits. That also means that it is possible that shield percentage also shows their efficiency - so, shields at 100% will stop all of energy directed on target, but shields at 30% will stop only 30% of energy that hits them - at least when it is about energy weapons. That is only theory, thought. Also, screenshot below seems to confirm that shields are at least partially graviton-based; that is possible, since majority of powers uses particle-based weapons (disruptors, phasers).
That my theory is confirmed by "Besto of Both Worlds". When Borg fire shield-draining weapon on Enterprise, Worf reports: "Shield effectiveness has been reduced 12%". After second shot, he reports "Shields have been reduced 41%".
Shield frequencies and modulation
Here we have 3 things:
-confirmation that shields are indeed graviton-based
-energy output of shields
-shield modulation
Second value is most interesting beacouse it could give us strength of Galaxy-class starship's shields.
As we see here, cochrane is unit for subspace distortion, implying that at least some of Federation weaponry might be subspace-based or have subspace-based component. Other possibility is that subspace field is used to "hold" gravitons in place. Gravitons are theoretical particles responsible for gravitation - theoretically, exchange in gravitons between two masses is what creates gravity. Given that most Star Trek weaponry is particle-based, such shields would be very effective, however, magnetic field is still required against EM-based weaponry like lasers (althought, given that laser beams are composed of photons, graviton shields would be at least partially effective - light itself exhibits properties of both waves and particles) [1] [2] [3].
So Star Trek shields have 3 components - gravitational, electromagnetic and subspace. Unfortunately, that means we can't accurately quantify their strength beacouse it will vary depending on nature of threat.
Also, shield frequency seems to suggest that Federation shields are not permament barrier, but that shields are turned on, shut down and then again turned on many times in second (257.4 million times per second as per screen from "Generation"). Star Trek weapons are also frequency-based, which explains possibility of weapon fire passing throught shields by matching frequency. Also, "regenerative shields" used by Borg and tested by Federation on USS Prometheus work by analyzing frequency of enemy weapons and matching frequency to completely stop weapons fire.
Case 1: shield and weapon frequencies are in perfect match. Shields stop weapons completely
Case 2: shields and weapons are in complete mismatch. Weapons pass throught shields unhindered
Case 3: most common case before advent of regenerative shields. Shields and weapons are in partial match only. Shields stop most of damage but rest passes throught.
Problem is with photon torpedoes - bleedthrought damage from "photons" should be severe if my theory is right, but it rarely seems to be greater than that of phasers. However, nature of shields might have something with that.
Shield strength from "Relics"
Enterprise-D held orbit in Cromosphere. Altitude was 150 000 kilometers (presumably from surface of star). Temperature of corona is more than 10e6 K (1 000 000 to 6 000 000 K at density of about 100 million to 1 billion particles.
"... the coronal cloud has a thermal energy of 10e51 ergs at 20 kpc..."
1 erg is 10e(-7) J. 1 kpc is 10e19 m or 10e17 km. At 150 000 km energy should be 3.9 x 10e46 J or 9.32 x 10e27 Gt over area of 8.98 x 10e18 square meters. Surface area of E-D shields is 321 700 m^2 when seen from side. Resulting absorbed energy is bit too high (1.397x10e33 J), so I guess I'll have to check all of calculations later.
(unfinished)
Shield geometry
Shields can have oval and hull-hugging shape.
Other uses
Photon torpedoes are also shielded; not only they can pass throught shields by using right frequency - only possible if torpedoes themselves are shielded - and sit in core of star for several minutes or dig in planet's crust - but we saw ship in TOS episode "Journey to Babel" which increased strength of its shields enough to make shields glow just like photon torpedo.
NOTES
In TOS episode "The Changeling" Spick reports that "We just absorbed equivalent of 90 of our photon torpedoes. Shields can withstand 3 more such attacks. Fourth attack will shatter shields completely." So TOS shields can absorb equivalent of 360 photon torpedoes of that era.
Shield pages on my site:
http://picard578.hostoi.com/startrek-vs-starwars/star_trek/space/starship_tactical_systems/shields/deflector_shields.html
http://picard578.hostoi.com/startrek-vs-starwars/star_trek/space/starship_tactical_systems/shields/regenerative_shields.html
NOTES
In TOS episode "The Changeling" Spick reports that "We just absorbed equivalent of 90 of our photon torpedoes. Shields can withstand 3 more such attacks. Fourth attack will shatter shields completely." So TOS shields can absorb equivalent of 360 photon torpedoes of that era.
Shield pages on my site:
http://picard578.hostoi.com/startrek-vs-starwars/star_trek/space/starship_tactical_systems/shields/deflector_shields.html
http://picard578.hostoi.com/startrek-vs-starwars/star_trek/space/starship_tactical_systems/shields/regenerative_shields.html
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