I'd suggest looking at super-capacitors.  I'm not an expert, but I think they can handle surges of power better than batteries and probably have plenty of capacity for a low-power computer and LCD display.

The problem with super caps is the truly dreadful cost per joule stored and low capacity.

Buying from Farnell a reasonable supr caps is:

Image is for illustrative purposes only.
Please refer to product description

 

Manufacturer:

COOPER BUSSMANN

Order Code:

2148519

Manufacturer Part No:

XV3550-2R7307-R

Technical Data Sheet (264.01KB) EN

Product Information

• CAPACITOR, SUPER, 300F, 2.7V, EDLC
• Capacitance:300F
• Capacitance Tolerance:+10%, -5%
• Voltage Rating:2.7V

Using three in series and working on a maximum of 2.4 V per cell you can store (7.2 * 7.2 * 100)/2 = 2592J but you can only usefully extract power down to 2V so the useful energy is 200J less : ie 2392J. The caps cost £12.10 each so the cost of three will be £36.30

Using lithium ion you could use Farnell part:

Image is for illustrative purposes only.
Please refer to product description

 

Manufacturer:

ENIX ENERGIES

Order Code:

1290995

Manufacturer Part No:

700001

Technical Data Sheet (147.83KB) EN

Product Information

• BATTERY, LI-ION, 3.75V, 2.2AH, PK
• Battery Size Code:(Not Applicable)
• Battery Capacity:2.2Ah
• Battery Voltage:3.75V
• Battery Technology:Lithium Ion

These are £19.92 each and store about 2.2 * 3.4 * 3600  = 26928 J. (The 3.4V is my estimate of a reasonable average voltage during  a complete discharge cycle).

The capacitors can take charge faster than the lithium batteries but you pay a massive price in money and capacity. The charge/discharge regulator for the capacitors is more complicated as well since the voltage swings over  a much wider range.

Super cap: £15.18 per kJoule

LIon:     £0.740 per kJoule

You can get LIon cells for much less from other sources.

I can't advise the OP on  a charger without knowing the power consumption of the computer and the endurance on battery power that is required.

MK

For this particular project, so far I have my arduino and a small 16x2 lcd screen. I plan to take the atmega out of the arduino and run it on a protoboard (for the sake of not dedicating my arduino for this project). I dont plan on adding anything else that would take up much more power.

LCD QC1602A v2 - www.e-licktronic.com/attachment.php?id_attachment=20

atmega328p - https://www.sparkfun.com/datasheets/Components/SMD/ATMega328.pdf

Small edit: I have always wanted to be able to effectively charge my phone on my bicycle also, so ideally I could do that off of these batteries also.

So after watching some videos on Lithium Ion charging, I've learned a lot. I am wondering if this would be an effective way to regulate the power coming from a generator on the bicycle. What voltage ranges would this system be safe at? Does this have any limiations?

If I used a large capacitor, I could minimize the effect of speed changing, and even stopping. Does anyone have an input on this plan, anything I need to keep in mind? This is all fairly new territory for me.

Possibly not  a (very) good way to do it.

You should consider using a switching regulator because the 7805 just wastes any extra voltage by getting hot. The 1000uF capacitor won't store much energy. If you are fit and your generator is good it might not matter that you are wasting some energy.

Can you set up the rectifier and capacitor and measure the voltage across the capacitor at typical and max pedalling. Then connect a load resistor across the capacitor (about 10R 10W would be right) and repeat. Then you can work out if you need care much about efficiency to charge your phone.

There are better linear regulators than the 7805 which is a VERY old design. (Newer ones don't waste so many volts so will work better at low pedalling rates.)

MK

So for charging my cell phone, Id want something along these lines?

http://www.ebay.com/itm/KIS3R33S-5V-USB-DC-7V-24V-to-5V-3A-Step-Down-Buck-Module-For-Phone-MP3-MP4-PSP-/321180084219?pt=LH_DefaultDomain_0&hash=item4ac7d327fb

I agree with Michael that a switching regulator would be much better.  I don't know what sort of voltage range you get from a typical bicycle generator or alternator, but it will vary a lot with how fast the wheel is moving.  The switcher efficiently switches higher voltages down to your 5V output voltage.  You might be able to get by with a lower output voltage for your phone or bike computer.

The eBay unit you show is the right idea, but it requires a minimum input voltage of 7V.  You should be able to find something with a lower input voltage.  You might also see if you can find a switching regulator module based on a "buck-boost" regulator such as one from Linear Tech.  A "buck-boost" regulator very efficiently converts from a higher voltage to your desired output voltage in "buck" mode and automatically switches to a less-efficient "boost" mode if your input voltage falls below your desired output voltage.  Some have very wide input voltage ranges, such as 2.7V to 40V for the Linear Tech LTC3115-1.

A 1000uF (1 mF) capacitor only stores 1 mC of charge per volt.  This is enough to provide 1 mA per volt for one second, or 100 mA per volt for 10 msec.  A larger capacitor increases this time linearly.  A capacitor has a limit as to how fast it can charge or discharge without damage.  I think this is called the "ripple current", but that's starting to exit my level of expertise regarding capacitors.  I suspect that a bicycle generator and your circuit are far from this limit.

Just to clarify the details a little bit. Putting aside the idea of charging my phone directly from the generator, could I use something like you linked to be the power source for a Lithium Ion battery charging ciruit? I want to design a project that will charge high capacity lithium ion batteries, and then I can use that power to do whatever I need to later on (i.e. charge my phone). From what I am researching, making a charging circuit is pretty straight forward using an IC like these. Powerstream has LiIon batteries that are upwards of 4Ah, and batteryspace has some upwards of 21Ah+. The batteryspace batteries seem to be missing protection circuits, which I know essentailly nothing about, but do know they are very important. Would it be a logical goal to try to take one of these large batteries, and charge it while im riding? Keep in mind, I ride up to 50 miles sometimes, so charging time shouldnt be a huge deal, I understand that it would take awhile to charge such a large battery.

Also, thanks for all this insight so far, you guys are help me a lot to understand all of this!

Mason Adkins wrote:

 

Just to clarify the details a little bit. Putting aside the idea of charging my phone directly from the generator, could I use something like you linked to be the power source for a Lithium Ion battery charging ciruit? I want to design a project that will charge high capacity lithium ion batteries, and then I can use that power to do whatever I need to later on (i.e. charge my phone). From what I am researching, making a charging circuit is pretty straight forward using an IC like these. Powerstream has LiIon batteries that are upwards of 4Ah, and batteryspace has some upwards of 21Ah+. The batteryspace batteries seem to be missing protection circuits, which I know essentailly nothing about, but do know they are very important. Would it be a logical goal to try to take one of these large batteries, and charge it while im riding? Keep in mind, I ride up to 50 miles sometimes, so charging time shouldnt be a huge deal, I understand that it would take awhile to charge such a large battery.

 

Also, thanks for all this insight so far, you guys are help me a lot to understand all of this!

Yes, those chips look reasonable.  I'm not an expert in battery changing, but the data sheet I looked at sure does make it look easy.

I don't know if bicycle generators have evolved since I used one last century, but it seemed like it had a lot of friction loss.  I wonder if you'd be better off with solar panels on a 50 mile trip?

Im looking into this really cool dynamo hubs, and from everything I have seen, they have come a long way from the original bottle shaped friction generators.