302 LEVERAGE!!!
Despite the apparent complexity of the field, almost the entirety of structural engineering is subject to the restrictions of the three primary stresses - tension, compression, and shear - and their subsequent failure modes. If Donovan could describe any of them as his 'favorite', it would undoubtedly be tension.
Tension was easy, or rather 'simple'. There were no edge cases with 'pure' tensile forces, nor were there a multitude of different failure modes. Structural components in tension were incredibly unlikely to fail unless their ultimate stress was reached, and the materials he liked to use tended to demonstrate physical signs of failure before a tensile failure. There was no need to account for Euler buckling, or crumpling, or local buckling, or shear planes, or block shear, all he needed to do was divide the tensile force by the smallest area it would apply to. Unfortunately, building 'up' tended to mean designs were controlled by compression, the weight of the structure pushing down on the foundation, or by a bending moment in one of the lateral members - technically a mode of tension failure, but measured by internal moment rather than lateral forces.
Construction was a different matter. Sure, lifting an object would require a compression member somewhere, but how that member was put into compression was not limited in the same way a solid structure would be. In fact, lifting objects a large distance was easier to do with a system in tension rather than compression, if only because materials with high compressive strength were difficult to make mobile - the only real options being levers, inclined planes, and pistons. A rope and a pair of pulleys are all you need for a tension system, and they are much simpler to design and maintain.
"Pull!"
The secret of the rope and pulley lay with the ability of a rope, any rope, to carry as much weight as the pulley can handle. A rope with a maximum safe tensile load of 100 pounds could be made to lift 1000 pounds by wrapping the rope around the pulley system five times. This effectively distributes the load from one rope to ten ropes, but more importantly reduces the amount of force needed to lift the object from 100 pounds all the way to 100. The tradeoff would of course be needing to pull the rope ten times the distance to lift the same distance, however this rarely tended to be an issue, the only cases Donovan could fathom being a limited length of rope or a limiting rate of pull.
He was limited by neither of those issues today.
"Keep pulling!"
Instead, Donovan found himself with the unenviable task of trying to get the legs to stick in their holes properly. Had he the proper equipment, this would have been easy. Unfortunately he was relying staked cables and his body weight to generate a rotational force, neither of which were looking to be strong enough.
"Hold!" The edge of the legs had begun to slide over the holes, a few feet of motion having taken much longer than he would have liked. Furthermore, the platform side hadn't risen so much as an inch off the ground, which did not bode well for his intentions to hoist it skyward. "Can I get a few of you to come over? We need to dig under the legs a little bit."
"How much do we need to dig?" Seppard, sweating profusely from his brief time tugging, stuck his shovel in the ground to support his body weight.
"Not much, just enough to get it off the ground." Donovan did a bit of math in his head. Regardless of where they stopped, their dirt fulcrum would compress. Not necessarily a bad thing given the desired direction was 'down', but if the legs got stuck in the walls of the hole they were going to be here for a while longer. "A gentle slope up to where the anchor stakes are. That should move the fulcrum back far enough for us to get some leverage."
"Anything else?"
"I'll need one of you to stay behind and help me set up the release mechanism on the anchor cables."
"What's that?" One of the men, a younger Nekh, tilted his head.
"I'll show you." Donovan waved him over while the rest started digging. "You'll be on the other side."
"Huh?" He tensed up, tail straightening and ears flattening. "I-I don't think I'm qualified to-"
"You'll be fine."
- - - - -
"So I just kick this lever when you tell me to?"
"With a bit of force, but yes. I would recommend you make big steps off to the side when you do though, once it starts sliding it isn't stopping for anyone." Donovan pulled on the cable to confirm it was in place. "The anchors should give before the cables snap, but if they do I need you to jump diagonally away from the point of attachment."
"Why?"
"Because a lot of energy just got released in a short amount of time, and it does not discriminate against flesh."
"Oh." Donovan sighed, watching the digging team with mild disappointment. Progress was being made, but Donovan had other things he wanted to get done today, among them the training of the assembled flight team. "I am sorry."
"Sorry for what?"
"I'm sorry we aren't as strong as you wanted."
"What I wanted was an impossibility, don't worry about it." Donovan ruffled his hair, only realizing moments after how patronizing that must have been for someone not much younger than he. "If the Holifanians couldn't match my expectations, I wouldn't imagine someone suffering like you to. All I need is to revise my understanding of your limits and work from there, no big deal."
"I see . . . thank you."
"If it's for saving your life, it isn't necessary. I won't treat you like slaves, but I do expect you to work for this favor. Neither of us can afford to slack off."
"What? I, no, that's not what I meant." Donovan raised an eyebrow. "I meant to thank you for viewing us as capable, for treating us with respect. I know we failed to live up to your initial expectations, but to have greatness anticipated of us is appreciated. Even if they don't say so openly, it feels like all we receive from the Holifanians and the Sanctum's representatives is pity."
Donovan eyed the young man up and down, wondering how to proceed. Even if he wasn't earning any points for job performance, Donovan quite like the mentality.
"That's something I understand quite well."
"Hm?"
"The feeling of unwanted pity. I get it." Donovan sat down next to him. "We're in similar situations, even if it doesn't feel like it."
"What do you mean?"
"You're losing your planet, your home, and a lot of your people are dying in the process. I've already lost my home, and I've lost everyone with it." Donovan sighed. "Different scenes of the same play."
"Oh . . . I'm so sorry, I didn't know."
"Is that pity I smell?" Donovan tilted his head, pinning the boy down with a tired glare. He instantly tensed up upon recognizing the irony.
"I didn't mean to-"
"Don't worry about it, just know that nobody else does either. They don't intend to insult you with their pity, so don't take it to heart. If you want it to stop, you've got to work hard enough to dispel it." Donovan patted him on the back before returning to his feet, stretching as he did so. "Fortunately for you, I've got the tools available to make that easy."
"Tools?"
"Yeah, how familiar with mechanics are you?"
"What do you mean?"
"The art of moving things with other things. This little system we've got here is a good example, how do you think it works?"
"Huh?"
"Come on, I'm trying to turn you into a problem solver here. Tell me how you think this system works." Donovan gestured with a sweeping hand towards the cables and pit. "It doesn't need to be right, I just want to know how you think it works."
"Um . . . the pulleys turn the top upwards while the anchor turns the bottom downwards?"
"Sort of, but let's get more granular. What is the anchor for, and why is it in that location?"
"It's there to keep the tower from sliding . . . but I don't know why it has to be there. Is there a reason?"
"Of course. If we put the anchor right next to the hole, do you think it would be able to resist as much force?"
"Oh, it needs to be that far back to keep it from breaking the ground apart?"
"Close enough. Now what is the pulley system for, and why in that location?"
"It is there to pull the tower up, and it is on the top of the tower to make pulling it up easier."
"So you've got the basic concept behind levers down, what about the pulley arm? Why is it there?"
"I don't know." At least he wasn't beating around the bush.
"The honesty is appreciated, but I want you to think about it for a second. Why would I want to elevate the pulling point?"
- - - - -
"- and so most of what you should be looking for is places where you can use mechanical advantage to let one man do the work of multiple, even if it takes him a bit longer than usual. Work is equivalent to the force times the distance that force acts over, so knowing where you can make the most out of those sorts of tradeoffs is important."
Diana picked up on the conversation from much further away than she probably should have been able to, walking towards the worksite of some thirty shirtless dirty men. It was Donovan she gravitated towards, naturally, though she did not recognize the boy sitting in front of him. It didn't take much for her to realize he was being educated, though the efficacy of such was in doubt given his confused countenance.
"I don't expect you to know where or when to apply these concepts immediately, just keep them in the back of your mind for when you find a useful situation for them."
"Y-yes sir." He nodded, coming to his feet as the men digging signaled they were finished. "Um, how will I apply them if I don't have the tools?"
"You can make them. A branch or boulder can work as an impromptu pulley, even it it will be a little harder to make work because of friction or an irregular shape. The same goes for levers and wedges, and most of the other machines besides screws and wheels. If you don't have a purpose built screw or wheel, it isn't worth using them. Now let's get into position. You remember what to do, right?"
"Yes."
"Good, Diana?"
"Eh!?" She stopped in her tracks. Still a few yards away from his back, Diana was certain she hadn't made enough noise to be heard, at least not by Donovan. "How did you know I was here?"
"You aren't as sneaky as you think you are. Please stay back by the Pegasus, I don't want you getting hurt if something breaks. Is everything alright?"
"Yeah, yeah, it's fine." She considered rushing in for a hug or something, but he was already walking back towards the tower and likely very sweaty. "I'll come for a kiss later."
"Love you."
"Love you too . . ." Frowning, she turned back towards the Pegasus, catching sight of a few curious onlookers off to the side.