Downfiring subs on carpet?

Should make no difference.

I have a short pile rug under my entire setup.

Polyester or wool?

I recommend installing one of these Auralex Acoustics SubDude Subwoofer Acoustic Isolation Platform underneath your sub. Very effective in reducing floor borne vibrations and helps tighten the bass. 

https://www.amazon.com/gp/product/B00COVEJ1E/ref=ppx_yo_dt_b_asin_title_o02_s00?ie=UTF8&psc=1

It doesn't cost much to try both.  Why not compare and report back?

Jon, That's my exact thinking. Due to arrive on this coming Monday.

The floor construction matters not so much the rug.

I use subdude on my upper levels with suspended plywood floors that will vibrate and muddy up the bass and obscure the midrange with most any sub. I also use them there under my bottom ported Ohm Walsh speakers for same reason.  

In basement with solid concrete floor foundation and dense but thin carpet and pad, not needed.

Anyone here recall the Stereophile reviewer who couldn't figure out why his system sounded funny until the cleaning lady confessed to replacing his rug with the fibers running the other way? Now what was his name? Oh yeah! Jonathan Scull! Also something about the torque of the screws on his CDP. Or direction? Something like that. Whatever. He was the champ. Until now.

Mapman is correct. 100Hz has a wavelength of 10 feet. The only way the carpet would effect the sound is by lowering the resonant frequency of the floor by adding weight but no stiffness. The trick with the floor is to get it's resonant frequency outside the range of the subwoofer. Concrete is the ultimate. You can get wood floors stiff enough by using larger laminated joists and doubling up on the plywood. Use construction adhesive on everything. What you put the woofer on makes absolutely no difference. My woofers are on concrete. If I play a 20 Hz test tone the whole house becomes a symphony of rattles. Fortunately music masks the rattles. Low frequency sound is very powerful. In terms of distortion the most important factor besides the driver itself is that the enclosure is stiff and very heavy. Ideally when you put your hand on the sub while playing you should feel nothing. No vibration at all. Having said all this you can negate most of these problems with room control as long as they don't boost any given frequency more than 5 dB or so. After that you start running out of power and digital headroom.

Hello markj941:

     Please don’t take the advice of those sub purists who recommend getting rid of the floor altogether, you may find the cure is worse than the disease, depending on what’s underneath your floor.
     It’d be very interesting and informative if you follow lalitk’s suggestion of a SubDude platform and jjon_5912’s suggestion to try your REL sub with and without it and then report back.
     I have no knowledge or personal experience regarding whether down-firing subs perform better on hard surfaces versus on carpet.  However, I do have significant knowledge and personal experience regarding the usage of single and dual down-firing subs in my system and room with wall to wall carpeting.
     Based on my knowledge and experience, I do have a couple of sub usage suggestions to offer you that are not directly related to your question but I believe you’ll still find them very useful:

   For best bass results,  it’s very important to precisely position your sub in your room in relation to your designated listening seat, especially if you’re going to initially utilize only a single good quality sub.  If you don’t currently own and don’t want to  Invest in the fairly expensive measuring equipment to determine this optimum sub room location, I’ve found ‘the sub crawl method‘ works equally well and it’s free.  You can google it for details.

     Through personal experience, I’ve learned that the generally accepted guideline, that the bass from 2 subs perform and sound about twice as good as a single sub In virtually any system and room, is absolutely correct.  Bass is cumulative in a room and utilizing 2 subs increases the in-room bass power and bass dynamics capacity when the source material calls for it, imparts a sense of ease and limitless to the bass and ensures that both subs are operating well within their limits.  The bass also sounds faster, smoother, more detailed and better integrated or blended with the main speakers.     This is also budget friendly, since individuals can begin with a single good quality sub and optionally add a 2nd sub in the future.

Best wishes,
  Tim     

I've got a slab of marble under mine and it seems to work Ok.

My pair of Zu Undertones sat on carpet for years. A couple of months ago I placed wooden cutting boards underneath them, and to my ears/brain, I think the sounds is more defined. 

I have down firing subs on a wood floor with a rug in front of the speakers, and a thick rug mat. I also found that isolating the sub and adding a second sub made big improvements. In my limited experience, I haven't found a difference in the front firing sub I've tried. 

Rather than a subdude pad, I used feet. SVS makes sub feet, but I went with platinum silicone isolation feet from Hudson Hi-Fi:  https://www.amazon.com/Platinum-Silicone-Hemisphere-Isolation-Durometer/dp/B075KM5Y8W/ref=sr_1_3?dchild=1&m=A3DXW0NUYLHI2J&marketplaceID=ATVPDKIKX0DER&qid=1588947657&refinements=p_4%3AHudson+Hi-Fi&s=merchant-items&sr=1-3&swrs=C706340B8638275BE0014217667F93CC

Rug mat:  https://www.amazon.com/gp/product/B01HN8MC4S/ref=ppx_yo_dt_b_asin_title_o03_s00?ie=UTF8&psc=1

It is very important that the sub can not move or vibrate. It should be coupled to the floor as best as possible. Spikes are the best whether the sub is on carpet or not. Right into the floor no pads. 

Coupling the subs to the floor would probably tend to increase the mechanical feedback problem, don’t you think? That’s why they invented isolation for subs and speakers in the first place. Hel-loo!

Three spikes please! Four can rock.

Hel-loo, subwoofers moving/vibrating = distortion. Put your hand on your sub as a real low note comes along. Ideally you should not feel anything but all of you will notice your sub vibrating to one degree or another. Geoffkait uses his sub for massages. 
Ideally you would mount your sub driver in a concrete wall. Some new designs like the Magico use two drivers firing 180 degrees from each other. This is called balanced force. These subs will not move at all and if the cabinets are stiff enough you will not feel anything while the sub is playing. The best way to keep most subs from vibrating is to couple them to a larger fixed mass, the floor. The best way to do this other than bolting the sub to the floor is with spikes. This would give Geoffkait an even better massage.

The entire room is moving, even if it’s on a cement slab. Hel-loo!