Hi TJ,.. that's a tough one. There's a lot of variables here like braking strength and tension on the machine, and tape type and condition on the tape side of the equation. For the most part, breaking tapes usually happen with either old acetate tapes ( very very fragile) or tapes that are damaged from poor long term storage. In stock form, the Technics machines brakes aren't strong enough for use with 10.5" reels and are better for 7" reels. The felt brake shoes that come stock won't grab unevenly and allow easy turning of the reels when threading the tape. when you shuttle to a stop (engage the opposite fast wind to slow before hitting stop) you're doing what the the machine does already, to a certain extent. When you hit stop, it engages dynamic braking (electronic) until the the tape slows down, then the brakes engage. You can hear this as a second click. The brakes (with whatever brake shoe material it has) need to be well adjusted so one side doesn't slow the reels faster than the other. And above that, your brakes need to slow the reels consistently and not grab. A good first start would be to clean the brake drums and then do an adjustment of the brakes. You'll need a service manual, an accurate scale, and a lot of patience to do this properly. If it hasn't been done, you may very well need some fresh brake pads too.
If you've been listening to lot of old tapes for a while and this is the first time your machine has broken a tape, there's a good chance that it's the tape itself. There's nothing you can really do about this but there's some precautions you can take. Make sure that all your old tapes have tons of leader. I'm not sure if you're a subscriber to the TP yet but the way that those tape are set up is ideal for old brittle tapes.
At the end and beginning of the tape is about a turn or two of white leader. Past that, there's a number of turns worth of blank tape. This way, when you rewind or fast forward, you'll see the leader ( I call it the warning track) that tells you when to hit stop. So, in effect, you'll never have to have the machine apply the brakes during a section that has the recording on it. Even perfectly adjusted machines can get out of whack so this makes it easy to avoid damaging any of your valuable tapes by putting any extra stress on the important part. A splicing block is an invaluable tool for anybody that collects old tapes.
Like I said, there isn't much you can do about some tapes since they may have old splices (done well enough that you don't even know they're there until they let loose) or lateral scoring from mishandling. If they're extremely valuable or one of a kind, I suggest doing or having high quality digital transfers made and minimizing playing them. One of the members here, Eric Jacobs, runs one of the very finest archiving and restoration facilities in the world and would be happy to help you if you choose to go that way.
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