I started with the fundamental scientific force that would be the key to making the entire concept work: Gravity. More specifically the acceration due to gravity. While I didn’t feel particularly lighter or heavier than I did back home, the engineer in me couldn’t take it for granted that this planet had the exact same gravitational constant as Earth. And since that constant would be used for the most critical of my calculations, I had to ensure I was working as accurately as possible to real world conditions.

The last thing I needed was my invention collapsing under its own weight.

That meant that after a quick breakfast and seeing both Phee and Devena off for the day, I headed with Yunni into town to conduct some experiments. After purchasing a hundred foot length of rope, a small leather satchel and a piece of slate chalk, Yunni and I set out to measure the highest point in the city that we could find. We ended up choosing the interior section of one of the high pyramid walls, which to me looked at least three hundred feet high. I touched the wall and tried using my scanning ability to measure it, but like I had assumed, it probably only worked with smaller objects. Luckily the rope would work just as well.

I stooped down and gathered five large stones from the base of the wall and then put them in a satchel. “Ok Yunni. Here’s the first task. We need to measure the height of this wall and then I need you to fly to the top and drop these stones down one at a time when I tell you to.”

“Got it.” She nodded enthusiastically as she took the satchel and then slung it about her shoulders. “How do I measure the wall?”

“Use the rope,” I told her. “Fly with it as high as you can and unravel it below you. When you reach its full length make a mark on the wall with the chalk. Then fly with it till the end reaches the point you marked. Tell me how many lengths it takes to reach the top.”

“Okay!”

The Nymph flew off with the rope and I shaded my eyes from the morning sun as I watched her carry out my instructions. Being as slight as she was, she fumbled a bit with the rope at first, but she kept at it and after a few minutes managed to get about half way.

“Keep going, Yunni,” I yelled up at her in encouragement. “You’re doing a great job.”

“Aye she is,” someone said next to me, and I looked to my side to see one of the city guards also shielding his eyes as he stared up at Yunni. “But what is it she’s doing exactly?”

“Oh hi!” I said. “Just measuring the height of the wall.”

“What for?”

“I’m going to perform a little experiment.”

“Experiment,” he said, furrowing his brow. “You got a permit for that?”

Uh oh…the last thing I needed was red tape slowing me up.

“Pretty sure we don’t need one,” I said as convincingly as I could manage. “It’s not like we’re doing magic or anything. Just a little math and science.”

Oratory vs Guard: Minor Failure

-10 to relationship

“Those sounds like magic words to me. Maybe we should take this down to the chambers for an opinion of a magistrate.”

Shit…I thought. I really had to get this guy off my back.

“Hey you know what?” I said. “I could actually use your help. Would you be able to keep the area clear for us, sir? It’s really important.”

Negotiation vs Guard: Minor Success

+50 to relationship

“Eh?” he said, seeming surprised by the request. “Why’s that then?”

The request for help had the impact I’d hopped. No better way to convince a man of the law that you are on the side of law, than by asking him for his help. A criminal mind would try to shoo him away, not keep him around.

“She’s going to be dropping some rocks from up there, so it’s best that we keep any civilians clear of the area to avoid anyone getting hurt. So it’s actually a good thing you came by, my good man.” I patted the guard on his shoulder while smiling. “I’m sure the goddess herself must have sent you to help us.”

Oratory vs Guard: Great success!

+100 to relationship with guard

“You’re quite right!” he said, puffing up his chest a little. “That could be dangerous.”

“Indeed,” I said and extended my hand. “Cole Jacobs by the way. Guildmaster. House Velmar.”

The guard eagerly shook my hand. “Third Guardsman Willy, at your service.”

“Well thanks for your help, Third Guardsman. We’ll be done soon.”

Willy made a big show of stopping people from entering the area. Much to my chagrin, by the time Yunni was ready to drop the first rock a sizable crowd of about thirty people had formed, eager to now see know why they we’re being stopped by the guard. The last thing I wanted was a crowd for this, but there was no turning back now.

“Okay, Yunni,” I shouted up to her. “Drop it when I say go.”

“Okay!” she yelled back faintly from high atop the high.

“And go!”

One-one thousand, two-one thousand, three-one thousand, four-one thousand, Five--

The rock landed with a high bounce and the crowd oo’ed and ah’ed.

“What happened?” someone asked.

“Did it work?”

“What was supposed to happen?”

“I don’t know.”

I chuckled inwardly. “Okay, next one, Yunni!”

We repeated the exercise four more times and I counted what I figured was about four and a half seconds on average. When Yunni landed with the rope, she balked at all the people standing around us. “What’s going on?”

I smiled. “Seems we’ve attracted some attention. What was your measurement of the wall?”

“Three and one third lengths.”

“Ok cool.” I smiled at Willy. “That’s it, Third Guardsman. We’re all done.”

“That’s it?” someone yelled out.

“What kind of show was this?”

“You stopped us for this?”

“What was the point of that shite?”

“I’m confused too,” Yunni said. “Why did we need to do that, Master Cole?”

I glanced about and nearly everyone standing there seemed waiting for me to answer Yunni’s question. I had a flashback to my Teaching Assistant days and I couldn’t resist the urge to share my knowledge.

“Okay,” I said. “Real quick. Let me borrow that chalk, Yunni.”

I began sketching on the inner wall. “Third guardsman, you don’t mind if I use this for illustration do you?”

“Uh… no, no of course not,” he said, as intrigued as everyone else now. “Go on.”

I started by writing a simple equation.

a=v/t

“So acceleration is what we’re after here,” I said turning about like a professor. “Specifically the acceleration due to a force known as gravity. That’s the force that makes everything fall down. Now acceleration or ‘a’ can be defined as the change in speed or velocity over time.” I pointed to the equation. “That’s V over T when expressed mathematically. You can also express this relationship as Velocity being equal to Acceleration times time if we re-arrange the equation, like so…”

I wrote that down next.

v=at

“If we use some calculus—which you all probably don’t know yet, so you’re just going to have to trust me on this—we can integrate to create an equation that can relate the distance that’s covered while an object is accelerating based on its acceleration. And it looks like this.”

s=1/2 at^2

“If we have a known distance ‘s’ and a known time ‘t’, we can rearrange this to solve for the acceleration like so…”

2s=at^2

2s/t^2 =a

“So now we just need to plug in the numbers. Yunni measured about 333 feet and I measured roughly 4.5 seconds to impact, thus we have...” I cranked out the figures in my amulet and not surprising the numbers were pretty close to what I already presumed. “32.88 feet per second squared.”

I wrote it out and circled the number

32.88 ft/s^2

“That’s pretty darn close to Earth gravity. Looks like our worlds are similar in lots of ways, Yunni.”

I gave her a smile and she stared back at me blankly, as did the rest of the crowd. It was so quiet, I could literally hear their brains clunking as they tried to decipher what I’d written.

“So this is your magic,” Yunni said more than asked, running her hand over my scrawling. “I’ve seen these incantations before…or what did you call them?”

“Equations?” I said.

“Yes equations. I’ve seen them before in the sacred tomes from your world.”

“This is magic?” someone from the crowd said.

“Must be some new kind of magic. I’ve never seen runes like that.”

“No!” Yunni said excitedly. “Not new magic. This is ancient magic! This is the magic of the Great Sage of house Velmar, the creator of New Haven and these very walls! And this is his successor, Guildmaster Cole!”

Yunni: Oratory vs Crowd: Success!!

Suddenly a new meter appeared in my vision as the crowd began murmuring with the same excitement as Yunni.

+50 to Reputation

You reputation within New Haven is now 50

People began bum rushing me with questions.

“Are you going to make the walls higher?”

“What does 32 mean? Is that the answer to everything?”

“It must be a lucky number!”

“A holy number!”

I had to literally push them back with my hands to keep them from mobbing me. “Ok, hold on, hold on. I can’t tell you anything now. But rest assured, if you’re interested in seeing what…magic…I’m creating with this, then be sure to be at the Expo in three days. Tell your neighbors and your friends. House Velmar is going to reveal something that will change all of new haven forever.”

Oratory vs Crowd: Great Success

+100 to Reputation

Current reputation in New Haven: 150

The crowd burst into more excitement and I ducked out of the limelight with Yunni in tow like a minor celebrity, avoiding more questions. Willy thankfully played interference and when I risked a glance over my shoulder back at the crowd, I saw the guardsman dutifully trying to disperse the onlookers as they ogled at my calculations on the wall. I nearly laughed at the absurdity of it all, but I supposed what I considered mundane could be considered magic here—same as vice versa.

“Now what, Master Cole?” Yunni asked as she tucked the rope into the satchel. “What are we to do with that magic number?”

I grinned at her. “Now, Yunni, the real magic begins.”

* * *

Back at the loft I cleared the workbench and Yunni stretched out a sheet of magic paper upon it that could project whatever I was seeing on my amulet. While the amulet was handy it was a bit like trying to draw on a smart phone. Once I linked the amulet to the paper, it was like working with a high resolution monitor.

“Perfect Yunni!” I commended her. “Now let’s get started.”

“Okay!”

“First, how many people live in New Haven? Do you know?”

Yunni tapped her lip thoughtfully. “The last poll there was about three hundred thousand residents, I think.”

I whistled. “That’s a good bit. Perfect.”

Before starting any design you needed to have a design basis—a purpose that would guild you to what needed to be build and why. This meant I needed to know how many potential customers to design for to determine peak capacity and average usage. I grabbed some text books and using Yunni as a sounding board, ran through my design basis, explaining to her what I was doing as I went along.

Using basic water industry standards, I knew the average person used around 20 gallons of water per day. So to service the entire population of New Haven that would amount to 6 million gallons per day. I probably wasn’t going to be able to design for that much right away, but if I was aiming to capture say 10% of the population, then that would mean a system capable of pushing out 600,000 gallons per day. That was my starting point.

I then worked my calculations back from there.

The first step was to design a means of storage and that meant using the old tried and true method of a water tower. Not only could a water tower store water but it could also store energy in the form of potential energy. That was going to be important to ensure service delivery; so that whenever someone turned on a tap, there would be an adequate supply of pressurized water available to use even if the pump failed or needed to be repairs or serviced.

The level of the pressure would be determined by the height of the tower. And now that I knew the acceleration of gravity was close to Earth’s, I could use some basic rules of thumb to determine that. For every 1 psi of pressure required roughly 2.3 feet of head, so if I was designing for a 40 psi water service that would amount to 92 feet. But that would be the base design. I’d also have to account for pressure losses through the piping too. As I didn’t have a detailed piping network designed yet, I would have to eyeball it and decided to put in a 10% contingency for losses. That mean a tower that was 101ft in height. I rounded it down to an even 100 ft for ease.

Now that I had my tower height I needed to determine the size and weight of the tank that would go on top of it. Only then could I determine the design of the tower itself. The size of the tank would be determined by how much water storage I wanted, which would act as a buffer for the pump.

Two full days buffer was probably be the maximum I could work with for now. That would give me two days to sort out any issues with the pump. That meant a 1.2 million gallon tank. Which was one hell of a big tank.

“Okay we got the basics worked out, Yunni,” I said stepping back from my scribble of calculations. “Now it’s time to start drawing and designing.”

Yunni was looking at the numbers mesmerized. “You talked to fast I couldn’t even follow you. But keep going! This is fascinating to watch. You’re like a genius!”

I laughed as I reached for the structural design text book. “I wouldn’t go that far, but thanks!”

I calculated the ideal dimension for the tank based on its volume. I started with a simple can shape, like the old school towers back in the day, but then I realized, they were only designed like that due to the limitations of construction back then. But with my melding ability, I had no such limitations.

I could make the tank any shape I liked.

Grinning, I threw away the basic 1800’s looking design and substituted a sleek bulb shaped tank for maximum volume versus material usage. Yunni boggled at what I had drawn.

“Is that the waterstone?” she asked.

“No, just a tank, but it’s just as important. I’ll design the waterstone next.”

I added more details to the tank, drawing an overflow system that would recirculate water back to the river. I then got fancy and turned it into an on-off control mechanism for the pump itself, so that it would automatically shut off and start the pump based on the water level in the tank.

I then began designing the tower structure, which was a pure joy to me. Normally, back home, firms would outsource donkey work like this to companies in China and India for their cheap labor rates and then just stamp it once it came back to head office. But now I got to do the fun stuff right from the ground up.

I was three quarters of the way through when Yunni suggest we take a break and volunteered to pop downstairs and bring us back some lunch. I ate one handed as I continued to work, moving from the tower to the pump.

This would be especially tricky, as I hadn’t worked on mechanical design since college, but after reading up for about an hour I had a simple design worked out. I started with the head pressure I’d need to get the water to the top of the tower. That was easy…100 feet of head. I then divided the 600,000 gallons per day by the amount of minutes in a day to get the same flow rate in gallons per minute.

I whistled at the number. “416 gpm at 100 feet of head. That’s a good sized pump.”

“What?” Yunni said.

“I’m going to need to see how much power I have available. Experiment time, Yunni!”

The nymph followed me outside to the river and I used the rope to measure out 100 ft.

“Okay same sort of deal as before,” I told her. “Only this time it will be horizontal. Drop a leaf into the river at one end of the rope and we’ll count how long it takes to reach the other end. That’ll give us the velocity of the water. I can use that to determine what kind of water wheel I’ll need to power the pump.”

“Okay!”

We performed the experiment a few times and I came up with a speedy averaged of 10 feet per second of river flow. That was a good amount of energy to draw from. We went back upstairs and I began designing the energy requirements from first principles.

The main one was that Work was equal to Force times distance or W=Fd. The other was the good old F=ma or Force equals mass times acceleration. In this case the acceleration was the acceleration due to gravity or the g which we had calculated and the distance was the height of the tower. Combining the two equations I came out with...

W=mgh

That was the amount of energy needed to lift any mass a certain height. But to determine power, I needed another factor. Time. The quicker the lift the more power that was required.

P=W/t=mgh/t

I went back to my flow calculations and worked out how much 416 gpm translated into mass per second. In this case the unit of mass was called a slug.

“Let’s see…” I twirled my hair while I paged through my text book looking for a reference. “How many slugs in a gallon of water? Okay, density of water is 1.94 slugs per cubic foot. And since there are about roughly 7.5 gallons per cubic foot…” I cranked out the number on my spreadsheet program. “416 gallons per minute equals 55 cubic feet per minute, which equals, 107 slugs per minute. Now multiply that by our fancy 32.88 ft per second squared for acceleration due to gravity on planet Grandia, and all that times 100 feet…equals…”

351,816 (ft . lbf)/min

I stared at the result on the paper. One horsepower was equal to 33,000 of those units. “Shit… that’s like ten horsepower.”

“Is that good?” Yunni asked.

I grabbed my mechanical design book next. “Let’s hope I can harness that much power from the flow of the river. I’ll convert that to Torque, send it through a gearbox and see what kind of moment arm we need to turn it.”

Yunni laughed. “It’s like you’re speaking a different language.”

I grinned. “I guess I am, kind of. I’m in full geek mode.”

“What’s a geek?”

“Um…” How do I describe this? “It’s like a smart person who is into also kind of awkward socially and who is into really specific non-athletic pursuits. Like reading books and stuff. Or playing lots of games.”

Yunni’s eyes went wide with excitement. “Oh my goddess, am I a geek then?”

I laughed. “I suppose you could be.”

“I must be,” she said, nodding emphatically. “I’m all the things you described, plus I have other pursuits besides just reading books. Although they might not be completely non-athletic”

“Oh yeah?” I said, my curiosity piqued. “Like what?”

Yunni smiled almost sheepishly and said, “To be honest, I research all these books about ancient artifact and magic because one day I hope to be able to write my own.”

I blinked at her. “No kidding. You want to be an author?”

“Well, an explorer really,” she said. “It’s why I joined the guild. One day I hope we get strong enough to be able to venture into the uncharted regions of the Vult. There are rumored to be whole civilizations, artifacts and ancient scripts that no one has ever seen before. Back in the Grand Archives I was relegated to merely dreaming of such things, just like the rest of the scholars, but now I hope to actually do it. I know it probably sounds a bit foolish, especially with me being just a tiny nymph, but with strong people like Phee, Devena and especially now you as our Guildmaster, I think that maybe I might actually get a chance to live that dream.”

I smiled at Yunni and her enthusiasm. It was always interesting to find out what made people tick inside and for her the quest for knowledge seemed beyond fitting.

“Tell you what,” I said, taking her tiny hands into mine. “As soon as we get all this sorted out and we win that competition, we’re going to be heading right into the heart of the vult. And I, Yunni, will personally make sure that you’ll have the chance to live your dream. In fact, by that time, I’m sure we could even land an Imperial Commission to explore the area while we blaze our trail through the jungle.”

“That’d be amazing!” Yunni said, bouncing on the spot and my relationship with her increase by another hundred points. She threw her arms around me in a hug. “Thank you, Cole.”

I hugged her back with a loving squeeze.

“Okay” I said pulling away. “But we can’t go celebrating just yet. We have a long way to go before we can make that happen.”

“Right!” Yunni said, with a no nonsense nod. “Back to work with you.”

“Indeed,” I said with a laugh. “Now where was I?” I turned back to my scribbles to see where I had left off. “Right, I need to convert this horsepower into torque. That’s a measure of how hard you can turn something by the way.”

Yunni giggled and looked over my shoulder as I got back into my work.

The calculation for turning horsepower into Torque was easy.

Torque=(Horsepower x 5252)/RPM

Basically the bigger I could make the water wheel, the lower RPM’s I’d need to supply that horsepower. With the water flowing at 10 feet per second, that equaled 600 feet per minute. Based on the geometry of the dock, I determined the max I could make the wheel was thirty feet across which would give me a circumference of 94 feet, which would translate into 6.38 RPM. A pretty slow moving wheel, which would produce a lot of torque. But that was only the start. I then needed to calculate what kind of blades the wheel would need to maximize its power and efficiency. While a flat panel blade would be simple to make I needed to make it curved and sunk as deep into the river as possible for maximum efficiency. I ended up with paddles that were five feet wide that would give me hopefully upwards of 60% efficiency and provide more than enough power to drive the pump.

I spend the next thirty minutes trying to figure out the pump design itself. I had the power requirements but now I needed to translate that into a mechanical design. I started with the simplest pump I could think of; a piston driven positive displacement pump. The water wheel could turn a crank and it would work like an internal combustion engine except in reverse. Only when I started working on the volumes for the pistons, I realized that for the flow rate I needed, the pistons were going to be huge.

I sighed. “This thing is going to end up as big as a bus.”

“Is that bad?” Yunni asked. “What’s a bus?”

“Something we don’t want,” I said. “It will take a ton of metal to make it and it will have a lot of friction losses too, which will throw all my power calcs off too.”

I scratched my head, sighing again, but then just like with the tank, I realized I didn’t need to make the design simplistic just because I was in a fantasy world. I was a fully functional CAD/CAM machine and I could crank out any design I wanted to the nth degree of precision. And with this much flow requirement, a spinning centrifugal pump was the only way to go.

With renewed energy I pulled out the pump design handbook and started looking at pump curves. Using my Horsepower and Torque figures I worked out a low rpm design that would have the pump spinning at 1000 RPM for the amount of head and flow I needed. From there I worked backwards, designing a gearbox that would turn the 6.38 RPMs at the waterwheel through a series of high tensile gears to come out at 1000 RPM at the other side. The gear ratio was huge and the final design had the gears looking like one of those old time Penny-Farthing bicycles, the ones with the huge front wheel and tiny rear.

By the time I was finished, my mind was spent. It was late in the afternoon now and the sleek curves of the pump impeller was staring back at me on my workbench, giving me a headache.

“I think I’m done…” I said exhausted.

Yunni nodded. “I had no idea your spell casting took so much preparation. It’s no wonder the Great Sage was so revered. To spend so much time to make a simple waterstone. The dedication is astounding.”

I laughed. Yunni had stayed with me the entire time, soaking it all up, but I wasn’t sure how much she actually understood. From what she just said, I think she still had in her mind that this was all truly based on some kind of magic.

I had made good progress but I still had a ton of work to do. Besides just calculating the materials needed to figure out the overall cost I still had a whole slew of smaller components to design. Pipes, valves, faucets, a clutch and brake mechanism for the water wheel, plus tools to fix and manipulate all this stuff. Just the thought of it was multiplying my headache by a hundred fold.

“I need a break,” I said and pushed away from the workbench.

I stood but no sooner had a done so, did my headache suddenly turn into a migraine. I hissed in pain as the light in the room became blinding. The world began to spin and suddenly the floor jumped up and hit me.

“Master Cole?” I heard Yunni say as I rolled about in a daze.

I couldn’t speak, couldn’t see, my body going into convulsions.

“Master Cole!”

The last thing I remembered was Yunni shouting my name and then screaming for help.