I have a Cobra HG A1500 on a 1998 Ford Ranger. Due to clearance issues I cannot mount it on my roof, so I put it in front of my windshield by the wipers. Will this give me good enough ground plane to communicate with CB? I live in a mountainous area and haven't been able to get a radio check with anyone.
The center of the vehicle on a large flat metal surface is always the best placement for performance, but when that isn't possible, placement at any given point around the periphery of the vehicle has relatively little impact on antenna performance.
This is especially true if all of the various parts of the chassis and body are bonded together electrically. The windshield is electrically pretty small on 11 meters, and there are other conductive paths around the windshield that should mean that performance there isn't radically different than anywhere else on the vehicle.
The big issue is that how well various body panels are bonded together varies considerably from panel to panel and from vehicle to vehicle. The door especially, which in this case is going to be a big part of the ground plane, very often has a poor electrical connection to the rest of the vehicle from an RF perspective, because it's constructed to minimize sound conduction, which usually requires isolating mechanical connections with sound deadening (and electrically insulating) material.
It would probably be a good idea to run a bit of copper braid from the quarter panel to the chassis under the hood, and from the quarter panel to the door itself, to ensure that it's got a nice low resistance path. This is usually done by running the braid from one of the bolts on the door hinge connected to the chassis, to one of the bolts on the side of the hinge that's connected to the door.
The roof and hood may also be similarly mechanically isolated, so it would be worth using a multimeter to check electrical resistance between the antenna mount and a bit of bare metal on the roof and hood. If they show a resistance of more than a fraction of an ohm, bond them all together in the same way as I described for the door, using the chassis as your common conductor rather than running gobs of copper braid straight from the antenna mount to each body panel.
Beyond that, bonding the rest of the vehicle together, or locating it at any other point around the vehicle is not likely to get you an improvement in efficiency of more than a few percent, and probably isn't worth the hassle. If you were running a 100 watt HF ham radio, it might be a different story just for mitigation of RFI and protecting the radio, but on a 4 watt CB, it's not something worth sweating over.
Mobile antennas are always compromises. No matter where you put the antenna, your ground plane will never be "good". A good ground plane is flat, and extends out at least a quarter-wavelength in every direction, preferably more. A vehicle simply isn't big enough to make that happen on HF. This is the compromise that must be made for mobile operation.
The question is not if it's "good", but if it's "good enough". People have mounted antennas on the trailer hitch, on the lips of the hood or trunk, and on the edge of a door, and had results that were good enough.
The usual test for determining if it works well enough is to see if you can talk to people with it. But if you can't talk to people, we can't conclude the ground plane is bad. It could be all kinds of things, like no one is around to hear you, or the radio or some other component isn't functioning properly.
There are things you can do to check, with the right equipment. If you have a directional power meter, you can check that the radio is putting power into the antenna, and that not too much of it is being reflected back. That would rule out most kinds of malfunctions, and suggest the problem is just that no one is around to hear you.
Alternately you can find a situation where you know someone will be around to hear you. Find someone else with a CB radio, and do some tests within shouting distance. Then get farther away and see if you get reasonable range.
Well I don't really know the car and the specific antenna good enough to give a proper answer, but I can think of several general steps you could take to check if everything is working fine.
First see if you have any reception with the antenna. Listen to the band at different times of the day and try to see if you can actually hear anything. If you know of any regular nets or round tables you should definitely try listening to them and to see if it's working.
Next, you mentioned clearance issues. My advice would be to actually try to find somewhere an open area where you can park the car and do some experiments. Try placing the antenna right at the middle of the roof and right at the middle of the hood of the car. Check SWR in both locations. I'm no sure if Google is giving me good results for the pictures of the car, but from what I've found, it seems that the hood has greater surface area than the roof of the car, so it should be sort of OK as a ground plane. Try to make some contacts if you can like that.
Afterwards, try moving the antenna to a more preferred location and see how things change.
In my answer to the question I will augment the merged previous answers. I do not use a CB antenna but I do operate HF 3.5 thru 30 MHz ham bands using a Hi-Q 4/80 Screwdriver antenna mounted on the rear of my pickup truck as shown in the image below.
Although it is hard to see, above the center loaded coil is the top part of the antenna that extends about 3 feet or so above the coil. The top of the antenna is 11 feet, 4 inches from ground level.
Now, the best performance of this antenna is when operating on the 10-meter band which is similar to the CB band; although, the antenna mentioned by the OP seems to be a major compromise as a CB antenna (and, as Phil Frost says, all mobile antennas are a compromise).
For the best performance I have, I have bonded using copper strap conductors in about six spots under the truck -- bonding frame to metal cab and panel parts. Result -- significantly reduces the noise generated by the truck itself (ignition, computers, alternator, etc.). And, I assume that it has improved my ground plane but I have no actual experimental proof of that as I failed to do a before and after test as I did with the RFI problems of a mobile rig.
But, the ground plane itself of the truck is a significant part of the efficiency of the antenna. How do I know. I know because the signal strength (as measured by S-meter) and by cooperating hams during a QSO, is much better for the direction off the front of the Truck rather than the rear and even the sides. How much better? About a half S-unit better. In fact, If I am in a QSO while driving and the other station is off the front of the truck and I make a right hand turn then that signal drops appreciatively. Indeed, I have lost signals entirely merely by the direction I travel -- it is like rotating a Yagi beam antenna.
Mounting dead center of the vehicle is probably the best as mentioned earlier but that is very impractical for many antennas, especially those trying to cover HF frequencies. Mounting below metal though is also very bad such as mounting in the bed of my pickup truck. Having a position high and clear from as much metal as practical that is below the antenna is best which justified the position I used on my truck.
I have made QSOs to the Falkland Islands, Indonesia, and other far off DX locations from my truck using this antenna and my Icom IC-706 MkIIg 100-watt rig. Also, I have contacted Cuba (from Washington State) via mobile CW on three different occasions from my truck. It works well for North American contacts too. Most of my operating though and all of the above examples were on 20 meters.