Yeah, I think you're better off constructing your own cabinet instead of purchasing a sub and sticking it in the hole (leave that alone guys
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That probably puts you at a usable cabinet of 1.8cuft. That is smallish for a vented sub, which from what I know, you'll have to have.
The JL Audio 8W7 will work in that enclosure size. Perhaps somebody here can model the port for you. Thats not what I do at all. I could do it, but somebody would have to fix it.
The driver would mount on the top, the vent on the front at the bottom. obviously a shelf could be installed just above the driver to house your components.
The driver can be had for 270 and the o audio 500 watt bash amp can be had for 230, thats your budget plus shipping. You'll also need the materials for the cab and some accessories to get it goin. Figure 600 bucks. If that works, we can go from there and you'll have a fantastic sub.
That driver is a fantastic performer and will outperform many commercial subs at a much higher price point.
If you can come up with some better dimensions, post a question in the DIY section and have somebody model the 8w7. Actually, I'll start a thread.