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I have a magic carpet, but the only thing magic about it is that it flies where and how its owner directs it. No bubble around it, no other magic; she has to hold onto it.
I'm wondering how fast and high it can go. It is large - 3m x 4m (and very stiff) - and ALL other factors are based on using 11th Century Arab Renaissance technology level to help the rider.
There are two important limits I can think of.
Altitude
For a human just hanging out on a carpet, the effects of altitude may be noticeable at 3500 meters and perilous at 8000 meters. At 3500m a low-altitude-lubber might experience altitude sickness with increased chances of an edema as altitude increases. 8000 meters is the mountain climber's "Death Zone" so you probably don't want to be up there that high for too long, even if you aren't exerting yourself. Unless you want to fly over Mt. Everest, there aren't a lot of reasons to need to go that high. There really aren't many reasons to go over 4000 meters. The highest settlements are up at 5000m, but very few people live above 4000m.
Velocity
From personal experience, waterskiing in the rain sucks, so going through a cloud at 30 mph would be less than fun. Motorcyclists on the highway pretty much have to wear eye protection to see. If you didn't it would be uncomfortable, you would need some sort of glasses or visor. Also, it gets really cold at high speeds. All in all, I would suspect that the discomfort caused by going 100 mph would probably be limiting.
If you really had to get somewhere in a hurry and would tough out being a squinting, shivering mass for the duration of your trip, the next limit would be your ability to hold on. Lets say you lie down flat on the carpet with your head facing forward, and heavy clothes as tight as possible (given medieval technology). Assume a surface area of 0.3m^2 (about 3 square feet). The force of wind is 1/2*(density of air)*(v^2) in N/m^2. For 100 mph we have 44m/s->1210 N/m^2 -> 37 lbs pressure on you. For 200 mph we have we have 89m/s -> 4951 N/m^2 -> 152 lbs pressure. Now its pretty hard to hold on. These calculations are not likely to be super accurate, since I'm counting your head as a flat wall, and discounting drag and such. But the numbers match what you'd guess from riding a motorcycle, I'd say that between 100-200mph is your hold on limit. At this point your gloved hands have a death grip on the rug's tassels to get any kind of hold, and the high winds and cool air at altitude is rapidly freezing them to numbness. Probably better to relax back to a leisurely flying pace. You'll get there sometime, inshallah.
Height
Altitude sickness begins at about 8,000 ft (2.4 km), with more minor symptoms typically found at 5,000 ft (1.5 km) on up. Assuming it's just her there, riding the carpet she'll likely want to stay at a lower altitude than these heights.
Speed
She could reasonably do as Henry Taylor said by rolling it up, but even if it can't be rolled up I imagine a saddle could be fashioned, as well as something to strap her legs down. The fastest a horse has ever reached was about 44 mph (70 km/h), while a normal gallop is about 20 - 30 mph. This should give you an idea of what is comfortable to fly.
If there's no limits on how tightly she straps down herself, and how fast it can go, it's more about the acceleration. Most people can survive up to about 5G (49 m/s2) for very short periods of time without blacking out. Your carpet probably shouldn't accelerate (including changing directions) faster than this.
I don't think it has a service ceiling, specially since it is magic that keeps it afloat.
As for speed, there is only one way to find out. You'd have to fly so fast that ablation due to air friction becomes an issue. The rider would be in danger way before you attained that speed anyway, so unless you are planning to do a sketch on Jackass, you shouldn't worry about that.
Here's what you should worry about:
Being stiff (probably due to all the cheicals you put on it to protect your property against ticks, fleas and silverfish, and to keep it impermeable), I surmise it will bank to turn. The traditional picture that comes to mind when we think about magical carpets allows for VTOL, but for some reason I am thinking it has to pitch to go up. Given these characteristics, even for slow, tranquil flight I would suggest you sew some security harness onto the thing. Lawnchair Larry knew that safety comes first when it comes to flying on your furniture.
Also beware that the friction with air will charge the carpet and its passengers with static. This may have all sorts of effects and hazards, so be careful with electronics and discharge safely whenever you land.
Fire is also an important safety hazard, so the use of narguile's on the carpet should be strictly forbidden according to international aviation laws.
Some people may have carpet allergies (seriously), so be sure to always have some antihistamines on you for your passengers.
Last but not least, if you have to take a pet along with you, be sure it is in a box. Not only because their claws might damage the carpet.
Because the magic carpet flies how and where its owner directs, its maximum height and speed will be set by the perceptions and cultural mindset of its owner. For someone who is a product of the 11th century Arab Renaissance this is likely to be a maximum altitude of around one hundred metres and a maximum speed of no more than ninety kilometres per hour. At an altitude of one hundred metres this is well above the height of most ground structures like buildings which would come nowhere near that, and it's well above the tallest trees. While still being enough to the ground to have a good view of what you are flying over.
A maximum speed of ninety kph is reasonably comfortable, especially in a warm climate where it would be very pleasant to have warm air blowing over you, and while it is much faster than those noble horses the justifiably famous Arab steeds it isn't terrifying fast like several hundred kph would be.
Those are owner friendly maxima for frequent magic carpet fliers. It is reasonable to expect that most trips will be below the maxima, but if an owner does a lot of flying they might gradually push the envelope. Most likely owners will stick with flight characteristic they feel most comfortable with, and magic carpets being good and obedient servants will comply with their wishes.
if the magic carpet is stiff and rigid during flight, the simplest way to ensure you won't fall off is to bind cords or ropes around the carpet. When the carpet becomes rigid and stiff the cords or ropes will tighten around the owner to hold them in place for the duration of their flight. The cords don't need to be too tight, just tight enough to hold someone securely.
Left to their own devices magic carpets can easily cruise at orbital velocities, at least, one thousand kilometres above the Earth's surface. Unfortunately, few 11th century Arab Renaissance magic carpet owners can survive flights of that nature. However, over the generations the makers of magic carpets have worked tirelessly to ensure their magic carpets have all the latest safety features and designed to be user friendly. Their motto: It is better to travel in comfort than speed.
For a real answer, if you don't want to rely on pure magic, we need more details about the means of lift. If lift is achieved through some sort of bernoulli effect, as in airplanes, the performance envelope is going to be completely different than if it's magnetic or some form of electrodynamics. The change in atmospheric viscosity at altitude is different than the change in electromagnetic field potential, and is therefore going to create totally different limits at which the lift and propulsion crap out. So, the only possible answer is, "no assertion", pending further clarification.
The real physic answer is not much faster than 70MpH because over that you wont be able to stay on the carpet.
Now for not real physic:
king Salomon eat noon lunch in Damascus and supper at Media. 1734km in around let say 4 hours: 400-500 km/h
