Are 4*AA batteries sufficient to power my servos with the below rated amps

Hey hi guys. I am in the middle of a project and planning to power a servo with 4*AA batteries (Alkaline batteries) (in series) so that it gives around 6V.
So in 1 full cycle, I got 170 mA usage from my servo (I checked it by connecting my multimeter in series with the servo).

So an ordinary AA battery gives around 3.9 Wh of power. So with that, I got these calculations-
3.9 * 1000 / 1.5 V = 2600 mAh per battery
So as there are 4 batteries, the total power output would be-
2600 * 4 = 10400 mAh.

So as my servo uses 170 mA of power per cycle(or for a single time) therefore the servo should work (at 170 mah) for about 10400 mAh / 170 mA = 61.17 hours

So are my calculations right? If not, where did I go wrong?
Thanks!

With new, high-quality rechargeable batteries that's a realistic estimate. But I wouldn't expect any random battery to always approach this value. In reality it may be as little as half it, depending on what battery you get your hands on.

That's not technically correct. mA without time unit can never reflect the current draw of a time-bound period ('cycle'). However, if you assume that the current draw of your servo is constant at 170mA, you have a starting point.
However, some things may spoil the broth. For instance, servo's typically don't have a constant current draw, but will draw a far higher current as they start moving and whenever they stall. This high current draw may reduce battery capacity beyond the actual power consumed; the effective capacity of the batteries will be lower if you try to draw a lot of current from them, especially so if you're doing it repeatedly/systematically as would be the case when driving servos. So your estimate of 61-odd hours will be very, very optimistic. How much it will actually be in practice depends on (among others) the issues outlined above, as well as the behavior of both the servos and the batteries as the batteries discharge and their output voltage drops. Your servos may not be able to use the last drop of power in the batteries because by then, the output voltage may have dropped below the point where the servos still work.

You're on the right track with your calculations, but to get a more accurate estimate, you'll have to account for some additional factors.

It is not right. The entire battery will only have 2600 mAh.
When connected in series, 170 mA will flow through each battery and they will all be discharged after 2600 / 170 = 15 hours. This is in case the battery actually has 2600mAh.

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@Boffin you're right, it sometimes amazes me how I overlook the most essential things...

For a plastic geared servo allocate 800mA for servo stall current, for metal geared servos allocate 1A stall current per servo.

But you really don't want to stall them so you only ever see anything close to those values for maybe a few milliseconds when the servo starts moving. For calculating how long a battery will run the much lower running current ((170mA in this case) is what you need.

So @koraks for my batteries, I am using ordinary 1.5V li-ion batteries. So can I assume that their capacity would be around 1800 mAh? Is there any way I could accurately(or even closely) calculate its capacity?
For my servo, I checked the max current input and that is around 170-180 mA. So that the highest my servo ever goes. So I am taking that value as the current input. So then even in this case, can I assume around 45-50 hours of battery life?

So @Idahowalker 800mA is what the servo would take if you try to force it to not move right?

@Boffin I didn't exactly get what you mean. You mean that the entire battery (all the 4 batteries in series) would give only 2600 mah or current? Isn't that too low? As when I check for the capacity of a AA battery in the internet, it shows that each battery has around 2500 mah.

I don't know what it is. Lithium-ion batteries have a voltage of 3.6-3.7V.
You probably have regular alkaline batteries.

Yas, I mean. You can check this easily. Use your batteries one at a time and you will get 4 * 2600mAh battery. But in this case, the voltage will be insufficient for the motor.
If you connect batteries in series, you are increasing voltage, not capacity. Capacity is the amount of accumulated charge that the battery can release over a given period of time.

@Boffin Ohh yeah, I got it now.

So then what is the best way to power a servo (for a long time) other than a wall adaptor?

Use 18650 lithium-ion (real) accu batteries. Two batteries will give you 7.4V.
If you need exactly 5V, add a DC-DC step-down convertor.
You will be able to charge the batteries and extend the operating time.
18650

If mains power is not available, figure out how long you need the system to run and get battery capacity to match, even if that means a bank of lead acid units.

If you can use solar to recharge, your required capacity can reduce somewhat.

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Where is the best place to buy these batteries and the charger?
I saw the prices in amazon and they are like 9-12 USD each. Are they that expensive?
Also, if i use 2 of these batteries, it will last for about 40-50 hours according to my calculations right? As they have much higher capacity?

I do not know the price of Amazon. On Aliexpress, for example, the usual price for a 18650 with a capacity of 2500-3000 mAh is about $3 for a piece. Normal manufacturers are Varicore, Litokala, LG, Samsung, Panasonic.
Never take 9900mAh batteries, this is fake.
A simple charger costs $8-10.
If you need a more powerful source, you can connect 2-3 batteries in parallel, but only of the same type.

Is there any way I can charge them up with a micro usb? Like a board that is connected to the batteries and a female micro-usb charger?

Watch this to get started
Using Li-Ion Battery Pack for Long Range Flying

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So what I was planning to do was to use a TP4056 module and connect 2 18650 li-ion batteries in parallel and charge them. So that also works right?

I know simple and cheap board based on TP4056.
It gives 1A of charge current. You can connect 1 or two 18650s in parallel to it.
It will work, but longer.

Maybe something like this will suit you
DFR0564 USB Charger for 7.4V LiPo Battery
But I have never tried it.