One question, can E2 be used from STOBAR carriers?
In general, ski-jumps make it possible for heavier aircraft to take off than a horizontal deck allows. However, ski-jump launches cannot match the payloads made possible by high-speed catapult launches. The catapult assisted ships (US and French CVN) appear to use about 262/2.5=105m to 337/3=112m launch length.
Ski-jump ramp takeoffs are considered safer than takeoffs over a flat-top carrier. When a Harrier launches from an American LHA, it would finish its takeoff roll and begin flight at 60 ft (18 m) above the water. It might not have a positive rate of climb, especially if the ship had pitched nose down during the takeoff roll. Using a ski-jump ramp, a Harrier will certainly launch with a positive rate of climb, and its momentum will carry it to 150 to 200 ft (46 to 61 m) above the water.
An AV-8B Harrier with a gross weight of 29,000 lb (13,000 kg) on a 59 °F (15 °C) day and a 35 kn (40 mph; 65 km/h) wind over the deck would require 400 ft (120 m) to takeoff using the 12° ski-jump ramp on the Spanish aircraft carrier
Príncipe de Asturias. The same plane would use the entire 750 ft (230 m) length of the
Tarawa class's flat flight deck.
The U.S. Air Force has examined the use of ski-jumps on land to enable short-field takeoffs. This was seen as "a possible solution to the runway denial problem in Europe" during the Cold War. When a ski-jump with a 9 degree exit angle is used, the takeoff roll of an F/A-18 Hornet can be cut in half i.e. from about 430m to 215m.
I believe the E-2D, which doesn't differ much from Hornet in terms of max weight, has a
Minimum takeoff distance of 410 m using ground roll.
Given the QE layout, it has a good straight full length runway, very close to 280m. The ski jump is angled at 13°.
For Kuznetsov/Liaoning, length is 305 m overall. On these ships, the ski jump is angled at 12°.
So, imho, if a ski-jump with this kind of angle halves minimum T/O run, it would appear possible to launch an E-2 from the Stobar carriers mentioned, assuming turboprops can give them enough speed (as compared to turbofans of F/A-18). Of course, if necessary, one could add JATO/RATO gear to aid take off if needed: these shorten take off run.
Relative performance would really depend on what the ski-jump adds, which in part depends on angle (and how much a 1 degree difference matter), and the difference a few meter more or less runway makes.
Given the deck layout of Kuznetsov/Liaoning, however, using a full length take of run may create an operational problem as there is no full length runway marked out: normal flight ops may be disrupted. But clearly, this is not a technical problem. With QE, one likewise wonders if that row of F-35Bs on the port side of the deck would still be possible when launching an E-2D. With a wing span of 24.56 m for the E-2 (as compared to 10.7 m for F-35B) and a ship beam of 72-73 m overall for all these ships, there a question of how disruptive the E-2D would be to flight ops.
Therefor, yes, I think it would be possible (though I'm not sure how optimal a solution it would be for STOBAR CVs)
_____________
JATO Bottle
A Lockheed P2V-3C Neptune launches with “jet-assisted take-off (JATO)” from the USS Midway (CVB 41) probably on April 7, 1949. U.S. Navy photo
U.S. Navy Lockheed P2V-3C
Neptune launches with "Jet-assisted take-off (JATO)" from the aircraft carrier USS
Franklin D. Roosevelt (CVB-42) on 2 July 1951.
_____________
Why would a country like France spends hundreds of million dollars to develop and build as few as three or four carrier borne AEW fixed wing aircraft for a sole aircraft carrier if they can buy with much lesser budget outlay from USA?
Spanish, Italian, British, Thailand all use ski-ramp, that rule out carrier based fixed wing AEW.
Brazil? Do they have the budget? Is the US willing to sell E2?
As on the carriers themselves, the French could cooperate with the UK, providing not only a similar carrier (PA2) but also a common AEW solution, which could possibly be exported to e.g Brazil and/or India.
While the QE class now has a skijump, it is designed to also be able to accommodate catapults, like US and French carriers. Recall the British government had intended to purchase the F-35C carrier version of this aircraft, and adopted plans for
Prince of Wales to be built to a Catapult Assisted Take Off Barrier Arrested Recovery (CATOBAR) configuration. After the projected costs of the CATOBAR system rose to around twice the original estimate, the government announced that it would revert to the original design.
Brazil has converted S-2T Trackers for AEW and for COD/Tanker roles and will continue using these on Sao Paolo for so long as she stays around.