Thanks Randy for filling in for me. great comment btw
Randy:
I don't mind being "flooded" at all, although I have to read the information two or three times before it all makes sense.
The power supply I linked to is actually 18 amps @ 12 volts. Based on your math, that will mean that the safe load is about 10 amps. I have already ordered two of the power supplies I linked to so I will order one more. Roughly, that will mean that each is operating at about 55% of max load. That will cover all the LED strips and individual LEDs plus the tortii. The DCC system will use its own power supply.
I think it will all still be within the capacity of the 20 amp/120 volt circuit.
This has been a very interesting learning experience. Just when I thought the light had come on, some more information comes along that tells me that the light was only barely glowing. Anyhow, thanks to all of you who have responded and Randy in particular, I think we have a viable plan.
Dave
Edit:
After taking into account your lower suggested power requirements for the individual LEDs and the tortii, the total draw will be around 30 amps. I had initially concluded that I would need 4 - 18 amp/12 volt power supplies based on your last post, but with my revised numbers using your lower draws for individual LEDs and tortoises, 3 will be fine. Even that is a bit overstated because I am using a figure of .4 amps/meter for the LED strips but the actual draw is .32 amps.
I'm just a dude with a bad back having a lot of fun with model trains, and finally building a layout!
South Penn:
I'm way ahead of you! I already have about 130 pieces of Code 100 Atlas flex track and 37 Peco Code 100 Electrofrog turnouts. I need another 60 pieces of track and two more turnouts. Man, do those helices ever eat track!!!
I have been purchasing turnouts and track ever since I had my layout plan more or less finalized a few years ago. I went with Code 100 because I was able to buy a bunch of brand new turnouts at bargain basement prices, and the slight difference in proportion doesn't bother me at all. I went with Electrofrog because I have several two axle critters that need the powered frogs to survive.
Thanks for the advice though.
If you would like to save even more money, consider going with code 100 track. Some will claim that the code 100 switches are not 'DCC compatable'. But as you are wiring from scratch anyway, it is easy to make them DCC compatible. The throat of the switch is powered by the track. The main and diversing tracks are isolated from the switch, both rails. Then the rails get their own power feed. Done!
How much can you save? I just bought a code 100 double crossover and it was $50.00 cheaper than the code 83. Switches run about $5.00 cheaper. 10 pieces of flextrack are about $20.00 less.
For electrcal protection ( the track ), I am considering using the cheap glass fuses in a cheap holder that you can buy in any hardware store. Normally a small tin of these glass fuses should last for years. And they are cheaper than a 1157 bulb.
It would be in the specs of the power supply. Otherwise you have to hook it up to some test equipment to measure both the input side and the output side, with variable load up to the rated maximum of the supply. The efficiency varies arcorss the load range - which is why people who buy a 1500 watt power supply for their computer and they only have 1 video card and a single CPU and one hard drive are absolutely silly - at low loads, switching power supplies tend to be inefficient. At 100% load it falls off again. Not to mention that a 1500 watt power supply ought to be on a 20 amp circuit, not a 15 amp.
Now, that unit you linked, the 110 watts is the maximum is draws from the 120 VAC side, which would be when it's under full load. So .92 amps at 120V, 9.2 amps 100% efficient at 12V. Actual efficiency you would have to find in the specifications. Pretty sure that's a switching power supply so in reality it will be somewhere around 75-85%. Obviously you will need several of those to get your total load handled - and power supplies are like everything else, you shouldn;t run them at 100% load, rather 75-80%. Assuming it's 75% efficient, that's a total of about 7 amps at 12V, so 75% of that for max load is 5.25 amps. So you'll need a lot of those to drive the layout lighting LED strips. I'd definitely look for higher capcity ones for that part of the system, so you didn;t need to use so many. Not one monster one though, for reasons previously mentioned - don;t want the whole thing going dark if one supply fails, plus you don't want to run long bus lines to power it all or you will get too much voltage drop because of the rather high current all those LEDs draw.
(stop reading here unless you want to get flooded with more EE stuff...)
In this you can see why the power lines that run across the country and eventually to our homes are as high a voltage as practical. As voltage goes up, the amps go down for the same number of watts - which is the work that power can do. And the fewer the amps, the lower the voltage drop in the transmission line. It's not quite as straightforward as calculating the drop in your track bus (and in fact the simplistic way we usually do this, assuming DC power, is not completely correct since DCC is not DC), because AC introduces other factors such as reactance (which is resistence dependent on frequency) and long parallel lines introduce capacitance which affects the reactance. For AC power transmission lines, this mostly just affects how much power comes out the far end based on how much is put in at the generating station. With DCC, running the bus lines in perfect parallel (physically - like using wire hooks always spaced the same distance apart) can introduce unwanted capacitance that in addition to increasing the reactance (resistence) in the wire, can also attenuate the signal. Granted, the whole thing connects to 2 rails which are by necessisty always the exact same distance apart - at low voltages and frequencies the effect is minimal, so normally we don't have to worry about it. That's why some suggest twisting the bus wires. Like twisted pair cabling, it reduces both the reactance and the crosstalk between adjacent wires. The snubbers you see mentioned to put on the ends of DCC bus lines, using a resistor and capacitor, work to optimize that reactance and the impedence (resistence) of the bus lines. A driver circuit like the output of a DCC booster, or a radio transmitter, will have a characteristic impedence determined by the specifics of the circuit used. If this signal is send to a system that is not properly matched, it's like the waves are out of sync, and push may be fighting pull - like if you make a ripple in the tub and then make another one not exactly in sync, they will partially cancel one another out. This ends up wasting energy being put into the system as heat. A bad enough mismatch can blow out the transmitter of a 5 watt CB radio. When you move up to HAM operation with 1000 watts, or consider a professional radio or TV station - it's VERY important that impedences match. In DCC all that might happen is we have loss of control because the signal becomes badly formed. When you're pumping thousands of watts into a system - that's a LOT of energy and bad things can happen.
It's not exactly the same, in radio and tv we're usually talking sine waves, not square waves, which have different characteristics, for one thing. And the frequencies are way higher with radio and tv. But the concept is similar. So don't be alarmed and think you need to do special things lest your layout go up in a smoking mushroom cloud. Far more critical to worry about basic electrical safety and keep all high voltage (120V) protected from accidental shorts, conact with people, and contact with anything on the low voltage side. Just like it's very bad if DCC track power gets tot he motor outputs of a decoder - it's VERY bad if 120VAC gets connected to the 12V DC output side of a power supply.
I'm sure I have some of this slightly off, it's been a long time. So don't take it as absolute gospel.
--Randy
Modeling the Reading Railroad in the 1950's
Visit my web site at www.readingeastpenn.com for construction updates, DCC Info, and more.
Hi Randy:
I think I came up with basically the same numbers except I didn't take into account the 50% efficiency factor. I calculated 434 watts at 100% efficiency (which I now realize is not possible). If I assume 50% efficiency that doubles the watts (right?) so I would need 868 watts total. You calculated 871 watts. I don't think the difference will cause the lights to go out!
That begs the question, how do I calculate the efficiency of a power supply, or do I even need to? I have no intentions of trying to convert used computer power supplies or anything even similar for the layout. I will use modern UL approved CCTV power supplies for the lighting like these:
http://www.canadacomputers.com/product_info.php?cPath=37_678&item_id=052150&sid=g1cgk0vm4l6cn74ru6hev1e6v1
The specs say that the units draw 110 watts.
I think the point is moot actually since apparently I will have lots of capacity with the single 20 amp 120 volt supply anyhow and the fused 18 amp/12 volt power supplies will distribute the lighting load over a total of 18 circuits, each with its own 2+ amp fuse.
Thanks for the tutorial(s) and your patience. My fear of burning the house down is much dimished.
hon30critter OK Lion and big daydreamer: I think I might actually have the picture. Load: 55 m of LED strips x .4 amps per m x 12 volts = 264 watts. 500 individual LEDs at .015 amps x 12 volts = 90 watts The DCC power supply will require 5 amps x 14 volts = 70 watts (max) The tortii (herd of tortoises?!?) will require 39 x .030 amps x 9 volts = 10 watts (or there abouts. I'm guessing at the tortoise draw). 264 + 90 + 70 + 10 = 434 watts total required Supply: 20 amps @ 120 volts = 2400 watts (less 20% for safety = 1920 watts available) 1920 - 434 = 1486 watts to spare (or there abouts). In other words the existing 20 amp/120 volt circuit is way more than I will need. Sorry it took me so long to figure that out. Thanks very much for your help. (electrically challenged) Dave
OK Lion and big daydreamer:
I think I might actually have the picture.
Load:
55 m of LED strips x .4 amps per m x 12 volts = 264 watts.
500 individual LEDs at .015 amps x 12 volts = 90 watts
The DCC power supply will require 5 amps x 14 volts = 70 watts (max)
The tortii (herd of tortoises?!?) will require 39 x .030 amps x 9 volts = 10 watts (or there abouts. I'm guessing at the tortoise draw).
264 + 90 + 70 + 10 = 434 watts total required
Supply:
20 amps @ 120 volts = 2400 watts (less 20% for safety = 1920 watts available)
1920 - 434 = 1486 watts to spare (or there abouts).
In other words the existing 20 amp/120 volt circuit is way more than I will need.
Sorry it took me so long to figure that out. Thanks very much for your help.
(electrically challenged) Dave
You're almost double on the Torotises - they are about 15-18ma each.
Don't convert to watts first, it just makes the rest harder to see. You still seem to be confusing the draw from the 120V side of the power supplies with the low voltage side DC current.
LED Lights: .4A/m X 55m = 22 amps at 12V
Structure LEDs: 500 x .015A = 7.5 amps at 12V (and you may want to use larger resistors for less than 15ma per LED, so they aren;t so bright it looks like a fusion reaction inside the buildings)
Turtles: 39 x .020A = .78A at 12V
DCC, 5 amps at 14V
Let's assume you use really poor quality power supplies that are ony 50% efficient. (I think even an old heavy transformer type supply does better than 50%).
Room lights: 22A at 12V = 2.2A at 120V with 100% efficiency. 50% efficiency means it woudl draw twice as much, 4.4 amps at 120V, or 528 watts (there are some other things that come into play like power factor - but this is WAY overconservative so we can ignore that for now - I can explain later)
Structure lights: 7.5 amps at 12V = .75 amps at 120V, 100% efficiency. At 50% this is 1.5 amps, 180 watts.
Turtles: .78A at 12V is .078A at 120V, 100% efficiency. 50% makes it .156A at 120V, or 19 watts (rounding up, bare with me...)
DCC: 5 amps at 14V = .6 amps at 120V, 100%. 50% makes it 1.2 amps at 120V, or 144 Watts.
So add it all up, you get 871 watts at 120V. Half the limit of a 20 amp circuit. That's worst case, crappy power supplies and rounding any decimals int he calculations up to the nearest whole number.
Hi big daydreamer:
I plan on powering the LED lighting strips through two CCTV 12 volt 18 amp 9 channel power supplies like this:
According to the specs the entire unit draws 110 watts @ 120 volts. The unit is "PTC" protected which should mean that each channel has an individual circuit breaker rated at a little over 2 amp capacity @ 12 volts. The LED strips are rated @ 2 amps @ 12 volts for every 5 meters (.4 amps/meter) but the actual full draw is 1.6 amps.
I will actually only need 12 channels in total for the layout lighting itself so the extra capacity can be used for room lighting during construction.
Does that setup make sense to you?
ok its looking better. I am a bit concerned about the 22A for the room lighting though. Are they going to all be connected in parllel?
Edit: You may need a lot of Amps for the room lighting but it would be good to if you can bring the number down by organizing things more efficiently. It was also previously mentioned that room lighting be powered independantly from the layout and I think that may be necessary considering the high demands of the room lighting.
I checked out some wall adapter power supplies and the highest im seeing is 250W. http://goo.gl/KuI11d
hon30critter Rich: Here is the main level of the layout:
Rich:
Here is the main level of the layout:
If you want to keep that mainline running at all times, it would make sense to create separate power districts for the engine servicing facility, the yard, and the track configuration at the lower left. So, the mainline would be its own power district, in addition to the separate power districts for the engine servicing facility and yard.
I confess that I have not closely studied the track configuration at the lower left. You have indicated that it includes two reverse loops and one or more helix. So, that may require more separation of power into addtional districts.
Rich
Alton Junction
BroadwayLion hon30critter Lion: I do plan on using an electrician. Before I go too much further I have to find out if I can get another 20 amp circuit out of my panel, which is 100 amps total. I had the panel replaced a couple of years ago and I had the electrician install an additional 20 amp circuit into the garage. At the time I thought that would be plenty but now I'm not so sure. Anyhow, my days of working inside the fuse panel are over! Dave You are confusing HO scale amps with 1:1 scale amps. 1:1 scale amps are at 120 volts,HO scale amps are at 12 volts. The entire layoutroom of LION runs aon a single 15 amp fuse, inculding the lighting. Many more amps than that on the layout, but they are at 12 volts not 120 volts. Just like mane fuses to the Abbey are 100 amp out on the power pole (4000 volts) there are about 4 200 Amp panels, 10 100 Amp panels and many many others. Our ememrgency generator puts out 100 kW; our normal draw is about 20 kW, 40 kW on Sunday (When the church is all lit up.) Of course our draw from the utility (MDU) is virtually unlimited, as far as our kneads go. AMPS x Volts = Watts. (Or something like that) 20 amps at 120 volts = 2,400 watts 200 amps at 12 volts = 2,400 watts 100 amps at 4000 volts = 400,000 Watts (on one of three fazes) 100 amps at 120 volts = 3,333.333 Watts (3.3 kW) 100 amps at 12 volts = 2.777 Watts fusing, isns't it. ROAR
hon30critter Lion: I do plan on using an electrician. Before I go too much further I have to find out if I can get another 20 amp circuit out of my panel, which is 100 amps total. I had the panel replaced a couple of years ago and I had the electrician install an additional 20 amp circuit into the garage. At the time I thought that would be plenty but now I'm not so sure. Anyhow, my days of working inside the fuse panel are over! Dave
Lion:
I do plan on using an electrician. Before I go too much further I have to find out if I can get another 20 amp circuit out of my panel, which is 100 amps total. I had the panel replaced a couple of years ago and I had the electrician install an additional 20 amp circuit into the garage. At the time I thought that would be plenty but now I'm not so sure. Anyhow, my days of working inside the fuse panel are over!
You are confusing HO scale amps with 1:1 scale amps.
1:1 scale amps are at 120 volts,HO scale amps are at 12 volts.
The entire layoutroom of LION runs aon a single 15 amp fuse, inculding the lighting.
Many more amps than that on the layout, but they are at 12 volts not 120 volts.
Just like mane fuses to the Abbey are 100 amp out on the power pole (4000 volts) there are about 4 200 Amp panels, 10 100 Amp panels and many many others.
Our ememrgency generator puts out 100 kW; our normal draw is about 20 kW, 40 kW on Sunday (When the church is all lit up.) Of course our draw from the utility (MDU) is virtually unlimited, as far as our kneads go.
AMPS x Volts = Watts. (Or something like that)
20 amps at 120 volts = 2,400 watts
200 amps at 12 volts = 2,400 watts
100 amps at 4000 volts = 400,000 Watts (on one of three fazes)
100 amps at 120 volts = 3,333.333 Watts (3.3 kW)
100 amps at 12 volts = 2.777 Watts
fusing, isns't it.
ROAR
LION beat me to it but I can still confirm for the sake of comfirming things. For pretty much any component you can calculate power sourced or disipated like this:
P = I×V
P = power [Watt]
I = current [Ampere]
V = voltage [Volt] Units are in brackets
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepow.html
I have a photo from a Yahoo DCC group showing a melted side frame on a diesel that melted from a short on a layout with 8 amp booster and the current limit was not exceeded. Posted by Allan Gartner. His link for wiring is right below.
No idea on how much current would be required to melt a side frame using a five amp system.
http://www.wiringfordcc.com/
If you ever fall over in public, pick yourself up and say “sorry it’s been a while since I inhabited a body.” And just walk away.
I think that the suggestion, that using a 5 amp booster can be dangerous, is misleading. If you use the proper size wiring for buses and feeders and solder feeders at recommended intervals, the use of a 5 amp booster on an HO scale layout should pose no problems even in the absence of circuit breakers set to trip at lower amperage. After all, that is the way that many smaller HO scale layouts are set up.
richhotrain I guess the problem I am having with that is the fact that a lot of modelers use a 5 amp DCC system to run a small layout with a single power district and no circuit breakers other than the booster. Nothing melts. Rich
I guess the problem I am having with that is the fact that a lot of modelers use a 5 amp DCC system to run a small layout with a single power district and no circuit breakers other than the booster. Nothing melts.
Talk to Cudaken and asked how that turned out for him.
There's two potential problems. One is minor, but the other is quite serious.
Problem 1: You have a gapped power district and because of wire runs and/or poor wiring, there is a slight voltage difference between Section A left rail, and Section B left rail. The difference in voltage causes the current to travel from the high voltage source to the low voltage source. That might be only .1 or .2 volts, but as you're crossing the gap, depending on how your left rail pickups are wired, you could be running .2 * 5 amps = 1 Watt. You better make sure your internal wires can handle that.
2. The more serious problem is when your wheel crosses the + and - legs at the same time creating a short condition at the wheels. That means you could have 5 amps crossing through your wheel. This will likely trip the booster. But if you have a problem combined with #1 above (like at a switch frog crossover ), then the booster won't trip but there could still be a large potential difference and wattage.jrbrenier also brought up an interesting problem in an old thread where the booster didn't trip during a short situation even though it seemed everything was wired up properly. It ended up burning out a booster or two if I remember.
It's always best to keep your districts to 3 amps or less in my book. That should be more then enough to run two long lit passenger trains with sound at the same time running at a good clip.
Don - Specializing in layout DC->DCC conversions
Modeling C&O transition era and steel industries There's Nothing Like Big Steam!
The Route of the Broadway Lion The Largest Subway Layout in North Dakota.
Here there be cats. LIONS with CAMERAS
Dark blue is the main line. Gray is secondary track including the yard and engine service facility. Various other colours are passenger track and caboose tracks (both red), yard lead (pink), arrival/departure track (light green). The medium brown in the lower left is an HOn30 mine which will be about 8" above the main line track. Turquoise is the leads to the two helices which will go down about 24" to the 6 staging tracks. The thin blue lines on the left represent a river. The river valley will be about 18" below the main line. There will be mountains in the upper left corner so I'm aiming at about a 33" - 35" total change in scenery evevation from the river bottom to the tops of the mountains.
Most of the action will be in the service facility, the yard, and the passenger tracks. I have designed the main line for continous operation and the staging will allow for several different trains to use the main line. There are several sidings which will provide opportunities for switching small cuts of cars.
The top and the right sides are against walls. The bottom and the left sides will have walls which are open on the outsides. Reach in to the helices, which are under the two reverse loops, and the wider sections of bench work on the bottom and the left sides will be allowed by installing flat panel doors in the back drop which will open away from the layout. The back drop won't be seamless but I can live with that. I can reach into the upper right, but it will be a bit of a stretch.
Any comments and suggestions would be very much appreciated.
hon30critter Sorry for the long winded answer. I need to learn to be more brief.
Sorry for the long winded answer. I need to learn to be more brief.
Here is my situation. My son is still living at home. He is 26 and has a really good job but unfortunately for me he is a fitness buff and half of the space I need for my layout is currently occupied by his exercise equipment. A couple of years ago we wanted him to get an apartment but we decided that paying rent would just be an impediment to him being able to save to buy a house. I have decided to be patient. Helping him establish his future is far more important than a model railroad. We do charge him room and board.
He and his lovely girlfriend have now saved enough money to seriously start looking at buying a house, and they have begun the process. Hopefully things will move along fairly quickly. In fact, local real estate prices are going up as fast as they can save money so there isn't much to be gained by waiting.
Once he has gone the garage will be mine. I will have to build a small shed outside to get some of the things that are now in the garage out of the way so that will have to happen first. I can start that any time.
I also just overcame another major impediment to building the layout, and that was cost. One of the reasons I have been asking all these questions is so I can come up with a budget. The initial figures were quite a bit higher than I had hoped so I was having second thoughts about building it at all. I discussed the costs with my wonderful and supportive wife and she said "go for it!".
I know many of you will suggest starting with a smaller layout but that just doesn't appeal to me. If I am going to do it, I am going to do it right the first time. I have spent the better part of 10 years designing the layout and I have what I feel is a plan that will work for me. I can't tell you how many hundreds of revisions I have made over the years but I believe I have been able to address the shortcomings. We shall see.
Dave, keep us posted on the progress of your new layout. When does construction begin?
Thanks Rich.
I'm realizing just how much I don't know about DCC, or at least I didn't know. Thanks to you guys that is slowly changing.
Dave, the PSX circuit breaker is an ideal choice. I use the PSX units on my layout.
If you have any reversing sections on your layout, use PSX-AR units to control those sections. The Digitrax AR-1 does not interact well with the PSX units.
And, yes, start out with one 5 amp booster. You can always add one later if that proves necessary.
In case you missed my edit to my last post, I did some more research on circuit protection and I learned that NCE has a CP6 automotive light bulb protection system but it seems rather primitive. I also looked up the PSX breakers and they seem like a much better choice.
I answered my own question about how many boosters I need - one.
Seems so simple when the light finally comes on!
The PSX breakers have an option to set them to manual reset, so the power won't come back on until you close the contacts with a pushbutton or similar.
To limit the current to any districts, protect it with a lower amperage breaker or fuse.
Randy and Rich:
Thank you! I now have a much better understanding of the logic behind power districts. You guys are being very helpful. I appreciate your time.
I don't anticipate ever having more than 3 operators. The walk in space simply won't be big enough to accommodate another person without people having to climb over each other.
Based on your information I should have at least 5 districts - one for each helix, one for the staging area, one for the yard and one for the layout main line and secondary lines. There could be a 6th for the engine service facility but that is probably overkill.
The answer to my next questions will be obvious to some, but I need clarification. I am planning on using an NCE system with an SB5 as the smart booster. I know that each district will have its own booster but does that mean that each booster will be 5 amps? If so, how do I limit the amperage going into each district so I'm not melting things? NCE seems to have discontinued the lower amperage boosters.
EDIT:
I went back and re-read the NCE information on circuit breakers and I learned that I can use a CP6 to provide separate power to 6 districts with just the Powercab and an SB5 smart booster.
I also researched the PSX circuit breakers and they seem like a much more intelligent system.
I have an NCE Power Pro 5 Amp system and have melted a couple of sets of Kadee metal wheelset. The booster and/or the power supply trips, but automatically resets in less than a second. ( Kadee now makes a 'plastic' side framed set of trucks. these prevent the short circut that the metal ones cause )
As I am upgrading the wiring of my layout, I am looking into breakers that must be maually reset or fuses. All of the breakers/fuses will be in the area of 2 Amp or less. The other concern is the capacitors discharging back into the track even though the power has been removed. I'm am looking for some guide lines in installing MOVs ( Surge protectors. ) accross the rails.
It all depends on your operating pattern. For example, you siad you will have a helix - the helix ABSOLUTELY should be a seperate power district, simply because if someone derails and shorts elsewhere ont he layout, if there isn't a seperate power district, the train in the helix will also come to a very sudden stop - and that's just asking for most of the train to leave the rails. Hidden staging is another good candidate since you can't easily see what happened in there - though it's also not a bad idea to have kill toggles for each staging track so that people don;t move the wrong train by mistake - if someone wants to pull loco 1234 and its train from track 3, if they line up track 3 and it turns out 1234 is actually on track 2 - derailment and mess as it runs the switch. With kill switches, you line track 3, turn power on to track 3, and if nothing moves when you dial up 1234 and try to pull it out, you know it's probably not on track 3.
Size of the layout does have some bearing on it, mainly because the larger the layout, the more trains you can have running at the same time, assuming enough people are around to run them all. So if you have multime trains all running on the main, with signals or with TT&TO, or whatever operating method you choose, if you break the main into seperate power districts, if someone goes on the ground between a-town and b-town, it doesn't completely gum up the whole works, the rest can continue to move up until the operating rules limits. Same with a yard. By keeping the yard seperated, a derailment int he yard won;t kill mainline trains, and vice versa.
How many districts and where they are located really depends mostly on your operating scheme. Once you get past the point of a single 5 amp booster running things, you'd add more boosters, but still subdivide those to more power districts. If you built a layount in an aircraft hanger but only ever ran trains by yourself, the only reason you'd have for power districts is the size - the voltage drop in such long bus wires, even if you use ridiculously expensive wire, would be too much, you'd have to use multiple boosters just to get basic power to all parts of a monster layout. But if you have a more modest 10x30 layout that is designed for 8 operators, you may need more power districts than a solo 12x25 operation. Same with total power requirements. The solo hanger layout needs more booster just to compensate for voltage drop, but if you think on more modest terms, the 10x30 8 operater layout will need more power than the 12x25 solo layout - yet both have the same effective area.
That's why there is no real "If you have X, you need to do Y" guide on power. There is no real one size fits all solution, even at the formula level. If you are building somethign that MIGHT eventually have large operating sessions, but for now it is going to be just you, my advice would be to at least wire it so that you can easily drop in more boosters and/or breaker sections - use terminal strips and break the layout bus up like it would be for multiple power districts, but for now just jumper over them. That way you don;t have to invest in tons of equipment that aren't necessarily needed for solo operation, but you also don't have go to back and rip out all the wiring and redo it if your layout becomes popular and you start hosting operating sessions. It's a modest extra cost to install the terminal strips but far less expensive than a couple of extra boosters and circuit breakers. Plus having the terminal strips can help debug wiring problems, you can easily disconnect a jumper and isolate a section of the layout to see if the problem is there, or a different section.
One reason for setting up power districts is to balance power consumption by "evenly" distributing power across the layout.
But, another important reason for establishing power districts is to keep motive power moving across the layout when a short occurring somewhere on the layout would bring the entire layout to a halt. Multiple power districts can isolate a short within the specific power district in which the short occurs.
So, "evenly" distributing power across the layout may not necessarily mean dividing the layout into 2, 3, 4 power districts of equal length. More importantly, power districts are established to isolate areas of activity from one another. On my layout, for example, I have separate power districts for the mainline, the passenger station and coach yard, the freight yard, the diesel servicing facility, and the steam engine servicing facility.