I use 23mm tyres on my H3s.
I'd advise checking what freehub body the rear has, to make sure of compatibility with the rest of your kit. My rear H3 has a freehub that couldn't take an 11-speed cassette - I think it was 9-speed. I bought an 11-speed EDCO monocoque steel cassette which fitted, but that's not a cheap option!

Robert

Check the alloy rim is firmly bonded to the carbon fiber - I had an alloy rim come unbonded on one of my older H3s, and it wasn't a cheap repair.

Robert

A Shimano 11-34 fits on a 8,9,10 cassette body

I wouldn't be surprised if the inner width is around 17mm.

The original HED 3/Spec Trispoke has been shown to be a very fast wheel, with the right tires and in the right fork. You may or may not have a fork that interacts well with the wheel and you almost certainly won't find a suitable tire. Even if you can get a narrow enough tire, it probably won't roll worth a darn.

Agreed. The tires you need to make this wheel work will impair performance beyond any aero gains you might achieve.

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The only tire that was fast aero and RR was the Bontrager Aerowing 19mm but the second run of production. They made them lighter and had a decent RR for a skinny tire. Doesn’t compete with the lowest RR clinchers now, but wasn’t that bad at the time. They were very aero bc the tire was as wide as the rim and the aero wing made the transition seamless.

I remember reading when tested with 23mm tires, they’re slower than most any other aero wheel. But with the Bonty AW they were the fastest at low yaw.

Unfortunately if given the opportunity now, I wouldn’t get them. you won’t be able to find the tires and if you do they’re likely old and not going to last long.

Any of the other Shimano 11-speed cassettes can be used on an 8/9/10-speed freehub body by removing 1.85mm from the back of the cassette.

I've had a front original H3 for about 15 years. You do need to run a narrow tire on it to take full advantage of the aerodynamic properties of the wheel, and the best option for that is the Continental Supersonic 20mm tire (it's even faster than the Bonty Aerowing). What type of racing are you doing? It's a great wheel for going really fast (low yaw) over short distances, but would you want to race a HIM or IM on a narrow tire?

This is what I am using for my front race wheel. When I got them they had Vittoria Corsa tires on them. I think they were 24mm (?). I put Continental Grand Prix 4000S 23m on them, then went the Continental Force Attack which are a 22m front and a 24mm back tire. Of the three setups I have had on them the Force Attack are my favorite. The Grand Prix and the Force Attack were the best options when I go into the sport 7 years ago, but things change. There are much faster tires now and instead of going to skinnier tires with high pressures for speed they are going to wider tires for speed now. I have done two races on the Force Attack and I will saw that I loved riding the front at 115 PSI and the back at 100 PSI.

I have a HED disk wheel for the back. No, I did not convert the HED 3 into a disc. It was a HED factory disc wheel. Both are aluminum brake tracks with I nice. I don't have to change out break pads when I put on the race wheels and they breaks actually stop the bike.

I did IM California on H3 aluminum brake track wheels, with Victoria Open Corsa 20mm F and 23mm R, both at 120 psi. I ran higher pressures to avoid pinch flats. It was rough over Babel Slough Road but otherwise OK.

Yup, I've raced plenty of IM races my aluminum H3. Would I now? I don't think so, especially if I'm looking to buy a set of wheels. I'd want something where I could take advantage of more advanced, wider tires with low CRR and not pay an aero penalty for using them. I haven't looked recently, but a set of HED Jet 6+ wheels with an aluminum brake track used to retail for $1K. I think they would have to be much less on the secondary market these days, and they'd give the OP a much wider array of tires to choose from.

i still ride my h3 for fun as i dont race and i have a flipping huge supply of supersonics both old and newer(still old now) probably won't be able to use them before they fall apart. at low yaw in tunnel was about same as a jet+ 90 with same supersonic 20 tire on both. at yaw it was a little worse. but i always got better times relative to competition on the h3 vs 90+ (annecdotal)