In my last post, I mentioned that there were some mechanical deficiencies that made my moped a little unsafe to ride. To address these issues I had to tear down the frame:

Before I built it back up, I took some time to do something I had been putting off: cleaning and resealing the gas tank.

The inside of the tank (which is in the down tube of the frame) had some rust when I got the frame. Since I no longer have any gas inside the tank, it is exposed to the air, causing it to rust even more. Even though I don’t have to worry about rust getting into the gas, I don’t want rust to eat through my frame, so I went through the process of cleaning out the rust and then coating the tank with a sealant. Since my tank is part of the frame, this is particularly difficult, and having everything torn off of the frame is the best time to do it.

So I began by creating a tourniquet where the petcock used to be to keep the cleaning solution in the tank. I filled it up with some Metal Rescue (which worked awesome -- highly recommended!) and left the moped in the garage for a day or two to let the solution work its magic.

After a number of rounds of letting the Metal Rescue do its work (and some shaking and vacuuming out of particularly pesky chunk of rust) I was finally ready to seal the tank. I used Kreem tank Sealant that I got from the independent kingdom of Treatland. The hard part was actually coating all the surfaces of the tank. After pouring the viscous sealant in and closing off the gas cap (with plastic wrap and rubber bands) I physically picked up and rotated the entire frame to get an initial coating. I then proceeded to prop the frame up in various positions against a tree in my front yard, allowing all surfaces to be coated. In this style, I applied multiple coatings, allowing each to dry in between. Afterwards, I had a nice white, non-rusty coating on the tank!

Alright! It’s finally time to put the electrical system on the bike already!

For my first test run, I opted to pretty much just throw everything in a set of saddlebags I “borrowed” from my roommate’s motorcycle. With the individual LiFePO4 battery cells organized into blocks of 4, I put one block in each side bag and two in the rear rack bag:

I also put the other electrical components in the side bags, including the controller and contactor (mentioned in my Control System and Electrical System posts).

As you can see, it wasn’t the most organized or refined setup..

Which, as it turns out, isn’t necessarily the smartest or safest thing to do. On one of my first tests in the driveway, a friend noticed some smoke coming out of one of the bags... some of my quick 12V wiring shorted out and the wire insulation burned up! No major crisis, but definitely could have been worse -- wire responsibly, my friends! I cleaned things up a bit after that little snafu.

So, with everything hooked up, I gave it a quick test in the garage...

It’s alive! It actually, kind of, sort of, works! The loudness that concerned me on that first test (if you listened to the video’s audio) was not actually an issue -- just a combination of chain noise and the motor with a trapezoidal wave controller, but that’s beside the point :-)

With that, one of my roommates and I took it to the streets! With him on his Tomos as my chaser, we took a couple videos in action:

This thing is a blast! It hits around 40mph, which was right where I was shooting for as my top speed. The torque of the electric motor gives it very good acceleration (for a moped, that is). You’ll notice I just have bike lights thrown on it for now -- I haven’t bothered to hook up the 12V accessories yet.

Once I was convinced that the electrical system was actually working, I decided it was time to take it for an extended trial run and test out its range. My round-trip commute to work is roughly 18 miles, so I used that as my first longer run. I wasn’t 100% sure that I would be able to make it, but I was estimating a 30-40 mile range so I was hopeful. Here were my key takeaways:

I’m still not sure of my range. I made it the full 18 miles, but it was definitely losing some oomph by the end of the ride. As measured by my Cycle Analyst, I used 20Ah of my batteries 40Ah. So in theory, I still had half a “tank” left, but it was starting to die. So I measured the voltages on all of my cells, and found that one was totally dead -- 0V. This explains why the system was starting to die when it “should” have have another 18 theoretical miles or so. Hopefully that means my real range is in that 30-40 mile target zone. Fortunately I had extra cells from the Chinese scooter I scavenged them from. Since they are used cells, I wasn’t surprised that one died on me.

This thing is a death machine. Its power and speed are about what I wanted, but other mechanical issues make it a little scary. When I got the moped its brakes were not very good, and that was with its original weaker engine. They’re definitely not adequate for 40mph without a lot of distance in front of you. This issue was exacerbated by the fact that the electrical system seemed to develop a new “throttle-sometimes-always-on” feature. With bad brakes and no kill switch mounted on the handlebars, that was scary. Clearly a cleaner re-wire is necessary. Last, the whole bike had some stability issues. In part, this is because I have heavy batteries mounted high (on the rear rack) affecting the center of mass and the handling of the bike. The other stability issue came from the front fork/shock. To put it simply, it was just a little bit wobbly.

As a result of (2), I decided to embark upon a massive mechanical overhaul of the bike, focused on safety. More info on that to come soon!

With that, I’ll leave you with one last shot of the bike showing off how weirdly bulky it was, bungie-corded to a pole to keep it from getting knocked over (aforementioned Tomos in the background!)

Before I talk about my experience putting everything together on the bike, I wanted to write a quick post about another “extra credit” component I added to my electrical system -- a Cycle Analyst:

The Cycle Analyst was recommended to me by a few different people and it’s definitely an awesome tool. It serves as a digital dash for your bike that provides tons of useful data. The Cycle Analyst displays real-time system voltage, current, power output, and cumulative Amp-hour (or Watt-hour) energy usage. This is super helpful for diagnosing any weird issues you might be seeing and for getting a feel for how much energy your system is actually using at any given point. It also has a sensor for your wheel to act as a speedometer and odometer as well -- all around a super useful addition to the system. There are some other features that the Cycle Analyst provides that I’m not taking advantage of or mentioning -- check out their site for more details.

There are a couple different variants of the Cycle Analyst; I got the High Current (HC) version of the Cycle Analyst V2.3 (the most recent available when I got mine). I bought one from Electric Motorsport, but it looks like you can get one direct from the manufacturer (with shunt, which I’ll explain shortly) for a bit cheaper. The regular Cycle Analysts are for lower-powered electric bicycles -- the HC is more appropriate for my system. 

Before going into how the Cycle Analyst is wired to the system, I wanted to talk about the shunt (pictured above) and its role in measuring system current. The shunt serves as a very accurate and low-resistance resistor that is wired directly in series with the circuit whose current you want to measure. It has two large terminals for connecting it in series with the high-power circuit, and two smaller terminals on either side of the shunt to connect to the Cycle Analyst to measure the voltage drop which allows current to be calculated. Having this external shunt allows for the flexibility of selecting a shunt designed to meet your system’s current needs, opposed to having the system’s current flow directly through your measurement tool like a typical ammeter. The drawback here is the need for calibration -- the shunt has a known resistance, which needs to be entered into the Cycle Analyst for its current calculation (I=V/R).

The wiring of the Cycle analyst is pretty straightforward. It comes down to just 4 wires -- power (V+), ground (V-), and two wires that connect to either side of the shunt to measure the voltage drop across it. The shunt is wired in series with the high-power circuit in between the negative terminal of the battery and the negative terminal input on the motor controller. As such, the ground wire and one of the shunt measurement wires are crimped together, so you only need to hook up the V+ to your positive battery voltage and the two measurement wires (one of which is combined with ground) to the two terminals on the shunt. Details on which wire is which are detailed in the manual. With these voltage and current readings, the Cycle Analyst can then calculate power (P=IV) and accumulate charge (Amp-hour) and power (Watt-hour) usage.

The last part of the Cycle Analyst I’m taking advantage of is the speedometer sensor. This is a magnetic sensor that you mount to the fork on your bike, and mount an included magnet to the wheel. When aligned correctly, the Cycle Analyst is able to measure rotations of your wheel. You must enter into the Cycle Analyst the circumference of your tire such that it knows the distance traveled per wheel rotation. While having a speedometer is obviously useful, this also allows for the Cycle Analyst to measure your energy usage per mileWatt-hours per mile (Wh/mi), akin to miles per gallon.

Now that we’ve talked about how the electrical system is supposed to go together from a power perspective, I wanted to touch on my specific system and how the control signals for the throttle and motor are connected to my motor controller.

I started out building the system on my workbench. Below, you can see the contactor (black box on the white paper) hooked up to the batteries (yellow) with a keyed ignition switch. Attached to one of the terminals of the contactor is a fuse (white cylinder). Here, I was purely testing out the functionality of the contactor along with the ignition switch.

In addition to all of the main electrical power setup that I detailed in my previous post, the control signals need to be hooked up to the motor controller as well. For my Kelly KEB72601 controller, everything connects using a “J2″ plug. From the Kelly manual, the pinout for the connector is:

The wiring diagram for how to use these pins from the manual is below:

Interpreting the wiring diagram above, the important pins for base level functionality (no regenerative breaking) are: 

1 (power from the battery, mentioned in previous post)

2 (ground, used for the throttle)

5 (0-5V signal coming from the throttle)

7 (5V output for the throttle and the motor sensors)

11, 12, and 13 (Hall effect sensors from the motor)

14 (ground for the motor sensors)

Below is a beautiful blurry photo of the J2 connector (metal cylinder below the socket wrench with a mess of wires coming out from it) as I crimped on some small connectors to the end of the wires noted above for quick connect/disconnect to the motor sensors and to the throttle.

Connecting the Throttle

The throttle I selected was a 3-wire potentiometer throttle. The idea here is that you send a ground (0V) and high (5V) signal on two wires, and the output wire will sweep from 0-5V based on the throttle position. At rest, the throttle will output 0V, and at wide-open throttle (WOT), the throttle will output 5V. So, pin 7 connects to the max throttle wire (5V), pin 2 connects to the resting voltage wire (0V), and pin 5 connects to the sweeping output voltage wire of the throttle.

For my specific throttle, I purchased a Magura throttle from Electric Motorsport. You shouldn’t. Their “documentation” was not super clear, but more importantly the throttle I received simply didn’t work. I thought I had made a mistake wiring the system when it didn’t work, but in fact the maximum voltage the throttle out out was so low that the motor controller didn’t even register it. Fortunately, I had another throttle from the XM Chinese scooter I had dismantled earlier and was able to use to that instead. Below is a video of me trying out the Magura throttle and nothing happening :(

Once I wired of the functional throttle, I was able to test out the wiring of my motor sensors...

Connecting the Motor Sensors

For brushless motors, there are Hall effect sensors in the motor that detect the current position of the rotor (spinning part). This provides the motor controller with the information it needs such that in can send the right power signals at the right time to the electromagnets on the stator (stationary part). These 3 Hall effect sensors will have output wires running from the motor to be connected to the controller, in this case pins 11, 12, and 13 of the J2 connector. You will also need to run power (pin 7) and ground (pin 14) to the appropriate wires coming from the motor. In the case of my motor, there was a diagram that indicated the different pins on a connector coming from the motor -- 3 Hall sensors, power, and ground. The diagram for my motor wasn’t super clear on the order (A, B, C) of the Hall effect sensors, and the diagram Kelly had for my motor confused the issue some more. I actually ended up trying all combinations of Hall sensor inputs to my controller in order to determine what setup actually worked. Below is a shot of the white board in my garage. In the bottom right corner, you can see the table I made for each combination of wires (letters indicated the color of wires I was connecting to one another). The starred line is was the one that worked best and that I went with going forward.

So far we’ve gone over all the major pieces involved in the electrical system for the moped: the motor, the motor controller, and the batteries. Now, it’s time to talk about how all these pieces connect and what other components are necessary to tie the whole system together!

First off, we need a fuse for the high-power (up to 48V, 300A) circuit. The specific fuse to get depends on your system -- I got a 400A fuse myself.

The next new component we need to talk about is called a contactor. A contactor is pretty much just a fancy heavy-duty relay -- an electrically controlled switch. The idea here is that we have a comparatively high-powered circuit that we want to safely open and close. A contactor is placed in between the batteries and the motor controller on the high-powered circuit. In its default state, the contactor is disengaged and thus does not connect the batteries to the motor controller. The contactor is controlled by a separate signal -- you can either use your full system voltage (provided your contactor’s “coil voltage” supports that high of a voltage) or a 12V accessory voltage. When you apply that voltage across the control terminals, the contactor closes and physically connects the high-power circuit, supplying power to the motor controller.

That brings up another piece of the electrical system -- we need a 12V circuit too! Although a lot of old mopeds used 6V systems for their accessories (lights, horn), 12V is the modern standard. Now that we don’t have an engine with an alternator/magneto, we don’t have anything to charge a 12V battery like a traditional gas vehicle would. For this we need a DC-DC converter -- a device that takes one input voltage and creates an output voltage. I mentioned previously that I got a DC-DC converter that accepts an input voltage of 24-72V and produces an output of 12V -- perfect for my system. (If you have a bit of an electrical engineering background and are interested in reading more, a buck converter is a good place to start.)

Now let’s first talk about connecting the 48V system: the batteries, the motor controller, the fuse, and the contactor (the motor connects directly to the controller, so we’ll touch on that later). To connect these components, we need to use adequately sized cables to handle the current. I used this tool to guide my decision on what type of cable to buy: http://www.solar-wind.co.uk/cable-sizing-DC-cables.html. I ended up using 4 gauge cables, as I had access to them already. A point of recommendation: make sure you get flexible welding cable for this. I picked up some 4 AWG at Home Depot, and it was very stiff and not useful for this project. I’m downgrading to 6 AWG on my next rewire (details to come later) and would recommend this or the equivalent gauge for your project. You’ll want to grab some appropriately sized lugs to crimp on too.

Once you’ve got your cables, the 48V system is pretty easy to hook up once you’ve got the order to connect everything right. My main point of reference is from the manual for my Kelly motor controller:

The 48V circuit here is along the dark lines around the border: the B- terminal on the motor controller connects to the negative side of your battery, the fuse goes between the positive terminal of the battery and the contactor, and the other side of the contactor connects to the B+ terminal on the motor controller. The diagram above also shows a “Key Switch” in the 48V circuit to control the contactor. Since I’m using my 12V circuit to control the contactor, I did not place a switch here, but instead on the DC-DC converter.

You’ll notice that you’ll also want a pre-charge resistor across the 48V contactor terminals. You can read a good detailed explanation as to why here, but the basic idea is that the resistor allows a small amount of current through the circuit which “precharges” capacitors in the motor controller, preventing a potentially dangerous/destructive large inrush of current when the contactor is closed. 

Similarly, there is a diode across the control terminals of the contactor. This is to prevent a voltage spike from damaging the motor controller when the contactor is disengaged.

Now we need to connect the 12V circuit. You can use the wire gauge calculator from before, but unless you’re putting some crazy high-power accessories on, 14 or 12 gauge from Ace or an auto parts store should do just fine. The DC-DC converter will have 3 wires: A ground (the two circuits will share a common ground), a high-voltage system input (48V in my case), and a 12V output. You can simply connect the ground and input wires to the negative and positive terminals of the battery, but I would recommend putting a switch in line as well so that you can turn off the 12V circuit (no need for a vampiric load to slowly drain your batteries when you’re not using your bike!). Once you have a 12V output, you can connect this 12V signal to the control terminals of the contactor (remember, your 12V ground reference is your negative battery terminal still) to close the contactor and engage the 48V system. I wired my system such that one switch provided power to the motor controller (connected to pin 1 in the diagram above) and to the DC-DC converter, thus in effect controlling both the 12V and 48V systems with one switch.

Wiring the power cables from the motor to the controller is pretty straightforward. With a brushless motor, there are 3 cables to run from the controller to motor:

Controller terminal “A” --> Motor terminal “U”

Controller terminal “B” --> Motor terminal “V”

Controller terminal “C” --> Motor terminal “W”

Make sure to use your heavy gauge cables for this. You will also need to connect your motor’s “hall effect sensor” outputs to your controller, as outlined for the Kelly controller in the diagram above.

Long time no post!

Some laziness followed by a mountain biking accident put me out of commission for awhile, but I’ve been making some progress on the Sachs and have lots of updates to share!

Long ago I promised a post about batteries, and I figured that should come before I talk about the entire electrical system.

Battery Chemistries

The first big decision when it comes to selecting batteries is whether you want to go with lead acid (like your car battery) or lithium (like your cell phone/laptop/tablet) batteries. Each of the two have different subcategories, but they all tend follow a trend with respect to weight, cost, and lifetime (number of cycles). 

Assuming the same desired battery voltage and capacity (in Amp-hours, or Ah), these trends are:

Lithium

Light

Expensive

Longer lifetime (more lifetime cycles)

Lead-acid

Heavy

Cheap

Shorter lifetime (fewer lifetime cycles)

A bit simplified, but typically the only reason you wouldn’t go with a lithium setup is due to the cost. That said, if you remember from my posts about the electric Chinese scooter I bought (part 1 and part 2), I managed to get a number of used lithium battery cells on the cheap. These cells were LiFePO4 cells -- lithium iron phosphate. This particular lithium chemistry is popular for DIY electric vehicle applications for a number of reasons; most importantly, it is known to be a very stable chemistry, making it a safer battery (no spontaneous combustion, for instance). 

Another thing to think about with respect to batteries is energy density vs power density. Energy density is what we tend to think about most often. This is the “capacity” of the battery, rated in Amp-hours (or Watt-hours, Wh, which is simply the voltage times the amp-hours -- more often measured in kilowatt-hours, kWh). The greater the energy density, the longer the battery will last on a single charge. This is usually the only important thing to think about when comparing battery sizes in mobile phones and other consumer electronics. However, electric vehicles are much higher power applications than your handheld gizmos and gadgets. Power is the rate at which we use energy, measured in Watts (W). Without enough power density, you will not be able to supply your motor with its full power. This rate of battery discharge is often defined using its “C” rating. The C-rating defines how much power the cell can provide by multiplying the C-rating by the capacity of the cell in Ah. For example, a 4C battery with a 20Ah capacity would have a maximum continuous discharge rate of 80A. Note that because of this, different capacity packs not only affect your range but also affect your maximum current output.

This power density is one of the other reasons LiFePO4 batteries are so popular -- while they don’t offer the same energy density as other lithium-ion cells, they provide a good balance of energy AND power.

For more info on different types of lithium cells, check out http://www.cobox-ebikes.com/296/basic-understanding-of-lipo-li-ion-and-lifepo4.html. This article also addresses lithium polymer (LiPo) batteries, which are good for high power discharge and can be used as well. Something to keep in mind though is that those LiPo batteries can catch fire when charging, and it is recommended to charge them in a fireproof charging bag. As a result, I would recommend LiFePO4′s for cells that are permanently mounted to your bike.

Charging and Discharging

Now that we’ve talked about some of the characteristics of different battery chemistries, let’s move on to how we actually charge and discharge your batteries. 

First, a quick note on voltage characteristics/lingo for batteries pertaining to charging and discharging that you’ll see in battery spec sheets:

Nominal voltage

This is the “named” voltage of a battery. It is measured as more of a midpoint of the actual operating voltage, as the actual voltage decreases as you discharge the battery.

Maximum voltage

This is the maximum voltage that the battery should be charged to.

Cutoff voltage

This is the minimum voltage that the battery should be discharged to.

Since I selected LiFePO4 cells, I will focus on those. For charging these cells, you have a couple of different options:

Single charger

The easiest and cheapest option for charging a LiFePO4 pack is to wire all your cells in series and charge the entire pack with one charger. I targeted a 48V system on my bike, which corresponds to 16 LiFePO4 cells. Unfortunately, this option is the worst for long-term battery health. It will charge the pack as a whole to the desired pack voltage, but there are no guarantees that each individual cell is charged equally, resulting in potential over-charging of some cells and under-charging of others.

Single charger with cell balancers

For better battery health, you can add cell balancers to each cell to ensure that each cell itself is charged appropriately. This works by diverting current through the balancer and onto the next cell when that particular cell is fully charged. 

Individual cell chargers

Rather than one big charger that you attach to either end of the full pack, you can wire single chargers to each of your cells. This will effectively give you the same result as the single charger with cell balancers, where each cell is ensured to be appropriately charged. In my opinion, this is a slightly less elegant solution since there is a lot more wiring to do and slightly more expensive than a bulk charger with balancers. An advantage is its configurability -- changing your pack voltage doesn’t require a full new expensive charger (rendering your old one useless in that application). You can simply buy the extra single chargers you need (or disconnect ones you no longer need) and you’re good to go.

Single charger with a Battery Management System (BMS)

This is definitely the heaviest duty solution, and will maintain battery health better than any other option. A BMS will monitor and control individual cells, ensuring optimal charging as well as discharging, while also providing other protections (such as temperature). These are pretty standard in higher power EV applications, but are costly and in my opinion a bit heavier weight than necessary on my DIY moped project. There are lower cost alternatives for lower power applications called Protection Circuit Modules (PCM) that seem appropriate, but I have struggled to find one that supports a high enough current output for my particular application.

All of this said, I chose to simply use a single charger with my pack without balancers or a BMS. This is because the cells I pulled from the XM had no balancers or BMS, and I figured some of the damage had likely already been done to the cells so it wasn’t worth the cost of adding any battery protection (yet, anyway). If I had bought brand new batteries, I would either choose cell balancers or find an appropriately-spec’d PCM for my setup. Both are reasonably easy solutions to retrofit, so I may choose to do so once I’m more confident about my batteries’ health.

Hola mi amigos!

I promised details about my drivetrain setup and some of the issues I was up against. For background, check out my post on gear ratios and my motor mounting posts (one and two).

So, outside of designing for the correct hear ratio, I also had to size my sprockets to clear the swing arm on the bike. When I mounted the electric motor, the drive axle of the new motor relative to the old engine moved. It it now further toward the front of the bike, and further to the ground:

You’ll see here the old yellow(ish) chain guard where the drive chain used to go through. I used a piece of thin rope to approximate how big of a sprocket I would need on my new drive axle to clear the swing arm and chain guard, assuming the same rear sprocket:

With this, I measured how small and how large the sprocket could be to still fit through the chain guard:

So, with that in mind, let’s talk about the numbers for my setup. The rear sprocket I have has 38 teeth. I’d prefer to keep this sprocket if possible, since getting a sprocket to fit an odd old moped isn’t necessarily trivial. My motor’s rated at 50 RPM/V, I plan on going for a 48V setup, and the outer diameter of my wheel+tire is 22 inches. Again, reference my previous post for the calculation of theoretical top speed. The corresponding spreadsheet can be found here. I’d like to have a top speed of maybe 45 MPH, so this would point to getting a front drive sprocket of 11 or 12 teeth. Unfortunately, these drive sprockets are too small with that number of teeth. Given the measurements I took, I opted for a 15 tooth drive sprocket. I will lose out on some torque by going bigger, but my motor is pretty overpowered anyway so I’m not too worried about it.

Another piece of background information: this moped originally had a 415 chain. It’s a somewhat weird chain that seems to only be used on mopeds. For some unknown reason, I wanted to keep using this chain size. This led me to get a #41 sprocket, which has largely the same specs as a 415 chain, except that the width of sprocket was a bit too large for the chain. Nothing a little grinding couldn’t take care of:

This is where the woes come in. Remember when I made those measurements for chain clearance? They didn’t account for the fact that chains don’t rest on the outer diameter of the teeth of sprockets -- the rollers/pins of the chain rest in the valleys between the teeth of a sprocket. As a result the chain sits lower than I was expecting, and I did not make the chain clearance that I needed.

At this point, I already had a larger front sprocket than my desired gear ratio called for, so I admitted defeat and started looking for a new rear sprocket. I measured the inner diameter (94mm) and found a couple options on my favorite treatland.tv (shout out to Benji at Treatland for his help!). I grabbed a 45 tooth one that didn’t have the right mounting holes, but those were easily drilled:

This time, I had two issues. For one, the chain clearance was still off a bit. The bigger issue, however, was that the offset of the sprocket (the distance between the surface that mounts to the wheel vs the surface that the teeth of the sprocket are on) was too large, and rubbed against the frame (the original sprocket was flat).

At this point, I contacted a friend in town that used to make electric motorcycles. He has an old 60 tooth sprocket that he said might work:

I had to get the inside bored out to fit my wheel (94mm), but I finally had a sprocket setup that had the right chain clearance!

Alright, let’s talk about the drivetrain of this sucker.

We need to transmit power from the motor shaft to the wheel. Just like a standard bike, we’ll throw a drive sprocket on the motor shaft, and simply use a chain to transmit the power to the sprocket on the rear wheel.

The size of the 2 gears relative to one another affect the torque and top speed of the bike. Given the same output from the motor, these two specs are traded off with one another. A bigger front drive sprocket will give you more top speed, but less torque, and vice versa. The rear wheel sprocket is the opposite -- bigger gives you more torque and smaller gives you more speed.

So, to calculate the theoretical top speed of your setup, you need to know a few different things:

Drive sprocket’s number of teeth

Rear sprocket’s number of teeth

The motor’s RPM/Volt rating

Voltage you’re running the motor at

The outer diameter (to calculate circumference) of your rear wheel+tire

To get the top speed, you need to calculate how fast the rear wheel spins, and multiply that by the circumference:

Speed in MPH = (RPM/Volt)*(Voltage) * (# front teeth)*(# rear teeth) * (outer diameter in inches)*pi * (60 minutes/hr) * (1ft/12inches) * (1 mile / 5280 ft)

I recommend a spreadsheet with this calculation so you can tweak the different parameters (probably the 2 sprocket sizes, maybe the system voltage as well) to see different theoretical top speeds. Remember that this is theoretical, and will be an overestimate. Feel free to take a look at mine here.

Obviously torque is important too, but to be honest I don’t have an intuitive feel for how foot-pounds of torque translate into real world moped performance :-P That’s the point where I chalk it up to trial and error if necessary, but the power of my motor (6HP) relative to the dinky moped it’s powering should give me plenty of torque when spec’d to a somewhat reasonable top speed. (Plus, I have pedals to get me going if I need a little help!)