Determining the energy efficiency of a Light Wand

Question

So, I'm working out some of the types of wands people can purchase in my flintlock fantasy setting, and I'm having an issue with one of them. Before I get to that, let me explain how Magic in my setting works. Arcane Magic utilizes an energy called Aethyr. It can do a wide variety of things, like shooting fireballs, levitating, and so on.

There's a magical industrial revolution of sorts taking place currently. Making magical devices is getting easier, so they are becoming more commonplace as a result. Among these are Spell Wands, a small wand that performs one or more simple Spells, usually no more than three, and almost always all a variation on the same Spell. An example: A Fire Wand can shoot a flaming arrow, spray flames like a flamethrower for a few seconds, or shoot a bead of crimson light that detonates on impact with the same force as a hand grenade. The Fire Wand can hold ten "charges." This isn't an exact amount of Aethyr, mind you; it is the amount of power needed to perform the least powerful Spell the Fire Wand can cast. So, the flaming arrow would require one charge, the flamethrower two charges, and the firecracker needs three in this scenario. Once the Fire Wand is out of charges, it doesn't work until it is replenished with Aethyr.

This brings me to my Light Wand issue. The Light Wand has 4 Spells it can perform.

Spell:

1. makes the tip of the wand glow for up to 10 minutes.
2. will leave a glowing bead of light the size of a grape floating wherever the tip of the wand was when the Spell was cast. (So, if you have it pointed at a spot in the air and cast the Spell, the bead of light will stay in that spot even after you move the wand away from it.) The effect lasts 10 minutes.
3. shoots a grape sized ball of light from the tip of the wand that will move in a straight line until it comes into contact with something, then stop and remain in that spot (even if the object that stopped it moves.) The effect lasts 10 minutes.
4. fires a beam from the tip of the wand. An object hit by the beam will have a glowing aura form around it for 10 minutes.

Now, my thinking is that each of these Spells uses a single charge. Where a Light Wand differs from a Fire Wand is that the intensity of the light generated by these Spells requires more charges. The Spells all have five settings, but I'm not sure what four of them should be and how many charges those four should require. To give you an idea of what I'm thinking, I'll put it like this.

Setting: 1. the light of a single candle 2. a 25 watt light bulb 3. a 50 watt light bulb 4. a 75 watt light bulb 5. a 100 watt light bulb

I've been trying to figure out how to measure the differences in intensity for these settings, but I need some help. I don't know of the intensities of the bulbs I listed are really the best ones to use. I know that the first setting is what I want as the baseline but what's a logical way of determining the brightness of the other settings. I've tried searching for how many candles it takes to equal the brightness of the types of bulbs I listed, but every source I find gives me a bunch of stuff like "well, are you measuring candelas, lumens, or lux?"

It's a magical bead of light the size of a grape that's floating in the air!!! How the heck should I know!?!

The thing is, assuming that a 25 watt bulb equals 25 candles would mean that the Setting 2 would require 25 charges, not 2, would it not? This is the primary issue I'm having. I need to figure out a simple way of setting up this Light Wand so that I can keep track of how much energy it has after my protagonist uses it in certain ways and also so the readers can grasp how it works without having to do a bunch of math. That's why I'm turning to all of you for help. Based on what I've described, what are five settings the Light Wand should have and how many charges would each setting require. Don't worry about the maximum number of charges the Light Wand can hold, though. The quality of the device determines that, so even if two Light Wands work the same way, one will have a larger "battery" than the other and require a recharge less often as a result.

So, what advice can you offer?

Update

Based on all the answers I've been getting, I've come up with the following:

Spell 1 = 1 Charge

Spell 2 = 2 Charges

Spell 3 = 3 Charges

Spell 4 = 1-4 Charges, depending on the size of the object illuminated by an aura.

The Spell will affect on object up to its maximum potential area of effect regardless of charges used, but the brightness of the aura goes down as the size increases unless more charges are expended. The largest size category won't be as big as a castle, but I think something the size of an Argentinosaurus would be acceptable, as that's roughly the scale of the bigger Monsters you'd want to highlight if you're fighting one in the dark. So:

1 Charge = Objects between the size of a grape and a watermelon

2 Charges = Objects between the size of a watermelon and the size of a horse

3 Charges = Objects between the size of a horse and the size of a T-Rex

4 Charges = Objects between the size of a T-Rex and the size of an Argentinosaurus

The base setting for each Spell is the intensity of a candle. We'll keep it simple and leave out any concerns with comparisons to modern light bulbs of any kind. The Light Wand has five settings that can be applied to each Spell. Each setting multiplies the brightness by a fixed number of candles. The multiplier cannot be tweaked beyond these five settings, as that would be too difficult for most people to manage without more than a basic understanding of using Arcane Devices. These are meant to be things an average person can use, after all. The settings (beyond the first 1 candle baseline) are:

25 Candles = 315 Lumens = X25 Charges

50 Candles = 630 Lumens = X50 Charges

75 Candles = 945 Lumens = X75 Charges

100 Candles = 1,260 Lumens = X100 Charges

Thus:

Spell 1 = 1 Charge, 25 Charges, 50 Charges, 75 Charges, and 100 Charges

Spell 2 = 1 Charge, 50 Charges, 100 Charges, 150 Charges, and 200 Charges

Spell 3 = 1 Charge, 75 Charges, 150 Charges, 225 Charges, and 300 Charges

Spell 4 (on an Argentinosaurus) = 4 Charges, 100 Charges, 200 Charges, 300 Charges, and 400 Charges

Now, that may seem like a lot of charges for the Light Wand to hold, but in terms of the actual amount of Aethyr used per charge, it isn't actually a huge amount of energy. It would really depend on the capacity of the Spellgem used to store the Aethyr. Further, since most Light Wands don't have all four Spells (they might only have the first two) and may only go up to Setting 2 at most, the cheaper models wouldn't need any high capacity Spellgem, making them much cheaper to produce.

I think that the highest caliber Light Wand, with all four Spells and all five Settings, would be able to hold a maximum of 1,600 Charges when fully energized. That amount of Aethyr would probably still be less than an amplified hand grenade Spell requires, since it's only generating visible light, not any kind of kinetic force or heat. And even at 1,600 Charges, the Light Wand would only be able to use its strongest Spell at the highest setting 4 times before it was depleted of energy. Not terrible, unless you're being attacked by five homicidal Argentinosauruses on a very dark night. You'd only be able to highlight four of them. Granted, the bright glow of those four might reveal the fifth one... provided it wasn't a ninja Argentinosaurus dressed in light absorbing spandex. (I wound how big of a katana it would use.)

The only real issue I can see with this is how the consumer knows how many charges the Light Wand has left. However, I can see some sort of indicator being featured on some part of the wand, likely above the handle, that the user can consult to see if the Spell he wants to use can be done at the setting he desires. A Mage, conversely, wouldn't need such an indicator, as they have an innate ability to gauge the amount of Aethyr a Spell is going to need. (Of course, a Mage wouldn't need to rely on a Light Wand in the first place, as a Mage can just cast the Spell himself at whatever potency he desires as long as he has sufficient Aethyr available.)

So, I think this is how I'm going to set up the Light Wand. Let me know if there are any issues you see with it or a simpler way to keep track of the energy in the Light Wand.

Answer 1

According to https://en.wikipedia.org/wiki/Candela#Relationships_between_luminous_intensity,_luminous_flux,_and_illuminance

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4π: a uniform 1 candela source emits 12.6 lumens.

https://en.wikipedia.org/wiki/Incandescent_light_bulb

The luminous efficacy of a typical incandescent bulb is 16 lumens per watt, compared with

60 lm/W for a compact fluorescent bulb or

150 lm/W for some white LED lamps.

Thus, through simple division you can calculate (imperfectly, yes, because of the differences between candelas, lumens, and lux but your readers won't care):

Incandescent: 16 / 12.6 = 1.3 candles/watt.

CFL: 60 / 12.6 = 4.8 candles/W`

LED: 150 / 12.6 = 11.9 candles/W

Now to the big problem with your specifications:

Setting 1 = the light of a single candle 
Setting 2 = a 25 watt light bulb 
Setting 3 = a 50 watt light bulb 
Setting 4 = a 75 watt light bulb 
Setting 5 = a 100 watt light bulb

The problem is that you do not specify what kind of light bulbs. (Since no light bulbs existed during the flintlock era, we shouldn't assume incandescent bulbs.)

You must decide what kind of light bulbs you are comparing your wands to.

Whatever kind of bulb you choose, you'll still have a problem, since -- for example -- a 25W CFL bulb is the equivalent of 25 * 4.8 = 120 candles. That's a lot of candles!!

So, what advice can you offer?

Drastically scale back the wattage equivalents for Settings 2-5.

Answer 2

Give each spell and each intensity a number that adds with the other to give the total number of charges needed.

Spells

You might be wondering why Spell 0 has no cost, we'll see why in a second. Spell 2 is the same cost as Spell 1 because they are essentially the same, but you can change this if you want.

• Spell 1- 0
• Spell 2- 0
• Spell 3- 1
• Spell 4- 1.5

Intensities

You can change the intensities when you figure out how much light you want for each.

• Candle- 1x
• 25 watt- 1.5x
• 50 watt- 2x
• 75 watt- 2.5x
• 100 watt- 3x

The math

Now, when you are casting the spell, you can use a simple addition to figure out the charges needed.

If you want Spell 1 with candle intensity, it's 0+1, which is 1 charge.

If you want Spell 1 with 25 watt intensity, it's 0+1.5 which is 1.5 charges.

If you want Spell 3 with candle intensity, it's 1+1, which is 2 charges.

If you want Spell 3 with 75 watt intensity, it's 1+2.5, which is 3.5.

If you want Spell 4 with 100 watt intensity, it's 1.5+3, which is 4.5.

Pros

The system is pretty simple, it just requires one addition.

You can adjust the costs as needed.

The 1/2 charges can be a plot point- you don't know if there are 4 charges left or 3 1/2, so you have to keep track carefully.

Using the decimals is much easier in addition than with multiplication where you could have .75 of a charge.

Cons

The numbers I am using right now let some of the numbers use half of a charge. You can allow use of 1/2 charges or you can change the numbers to whole numbers so you will not have that problem.

Answer 3

Factor in movement as a power cost.

Assume for a given power setting, the amount of light produced at each light effect is the same. 1, 2 and 3 look the same. 4 might be a larger object and if so, it will be dimmer than 1,2, and 3 because a larger area emits the same light as the grape in 1,2 and 3. If 4 illuminates a grape, it will look the same as 1,2,and 3 but be more delicious.

1. makes the tip of the wand glow for up to 10 minutes. At low power this costs 1, because light does not have to move from wand.

2. will leave a glowing bead of light the size of a grape floating wherever the tip of the wand was when the Spell was cast. At low power this costs 2 because the light has move from wand and maintain position.

3. shoots a grape sized ball of light from the tip of the wand that will move in a straight line until it comes into contact with something, then stop and remain in that spot. At low power this costs 3 because the light ball moves a distance.

4. Fires a beam from the tip of the wand. An object hit by the beam will have a glowing aura form around it for 10 minutes. At low power this costs 4 because the light must move and then the lit object might move.

With number 4 a very large object (e.g. a castle) might be invisibly dim. A small fast moving object (e.g. a bat) might be bright but possibly go out before the 10 minutes because of all the movement. #3 might also last less than 10 minutes if the ball must travel a very long way before hitting something (e.g. you fired it in the air like a flare).

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For brighter effect, multiply cost by desired brightness as multiples of baseline low power setting.