I split this from where you had posted it so it now has a topic of its own. Even though it was appropriate for where it was, I felt it needs more attention than it would get buried in another thread.
This question has been asked often and never adequately answered. That's because there are two aspects of this type of project. There's the electrical and the mechanical. Neither are simple to resolve. But it can be done. What follows is a basic rundown on the development of such a coil with the reasons behind each step. It's written to that the average reader can understand and is therefore missing a lot of formulas and tables that can easily be found by the technician or engineer.
First, the electrical issue. This won't change no matter how big your coil is. The first thing to note is that nearly every metal detector coil is an air core coil, meaning it is wrapped around a hole in its environment rather than around a metal form or frame. In framed or metal core coils, the magnetic field is kept inside the device by design. The magnetic field developed by the coil is focused inside the metal and aligned to maximize its effect in the circuit. Smaller coils for the same job is the result.
In our air core coils, the fields are expanded from the coil to the outside environment on purpose. Again, this is by design. The field has its greatest strength at the very edges and it expands into an ever weakening field to the top and bottom of the coil. For our purposes of generating the maximum field top and bottom, the air core coil is often fitted with something called a Faraday shield. This shield does much to focus the field energy in a single direction thereby requiring a less powerful device to energize the coil. The equivalent to this is something most everyone has seen. The cup magnet. This is a magnet that has a cup built around it with only one face of the magnet open to the world. This focuses the energy of both north and south poles of the magnet to one side, thereby doubling the strength of the magnet. Some Faraday shields are simply foil inside the top of the coil - much like a Frisbee with its inside covered with foil. Some are extremely thin foils wrapped around the entire wire bundle. They both serve different purposes for this discussion and are mentioned in passing.
The existing coil on your machine is matched to your detector electronics. In fact, the coil is an absolutely critical part of your tuned circuitry inside the electronics and must not be altered without a lot of attention being given to three circuit characteristics of your current matched coil.
1. Inductance - This is a measurement of your coil's ability to build a field charge. More inductance does not mean more field, however. The inductance value, when paired with the rest of the tuned circuit, is related to the frequency of the circuit and cannot be substituted without concern for the frequency of operation. In plain English, you can cause your detector not to function at full capacity if you vary the frequency. Inductance is measured in a unit called the henry. Coils have inductance ranging from around 180uh to 500uh. The u means micro so that is a range of 180 microhenries to 500 microhenries.
2. Resistance - This factor is entirely a DC value or entirely an AC value depending on when it is measured and why. For our purposes, it is a DC value related to the diameter of the wire (wire size) and the length of the wire in a coil. It is NOT FREQUENCY RELATED so matching the resistance in your new coil design to the original coil is absolutely irrelevant. I've seen some so called "experts" discussing coil resistance as if it is the only thing that is important when it is totally unimportant to the tuning. It is important that you remain fixed on this being the COIL resistance only. We do need to know the original coil resistance for another purpose which we will discuss later.
3. Impedance - This is an odd term and difficult to explain to a lay person. It is the entire circuit's resistance to the AC frequency applied to it. A tuned circuit, in perfect tune, will offer minimum (but never zero) impedance to the circuit supplying the power to energize it. It is a value developed from the total inductance, capacitance and resistance in a circuit (I told you we'd get back to this.). The circuit inductance is what we will strive to duplicate in our new coil design. This is an impossible task. I do mean that. So, rather than duplicate it exactly, we will use some techniques that allow us to substitute the coil with either the minimum of effect or with a minimum amount of redesign to your circuit.
I'm going to stop here because I don't know if there is a maximum to the post size here. I will pick this up later.
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It's all about that moment when metal that hasn't seen the light of day for generations frees itself from the soil and presents itself to me.
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