Wizards and Wastelands: Overview

I have recently returned to an old idea I use to kick around. One that let me don my conspiracy nutter hat. And what is a more awesome conspiracy topic than Nazis? So here is where far too many questionable Google searches led:

Hitler's suicide was a sacrifice used to fuel a spell aimed at the Allies. Unfortunately, the casting didn't work as panned, and delayed the effect by a century. Those Nazis who escaped criminal prosecution and execution at the Hague eventually discovered what went wrong and began constructing bunkers - vaults of information and supplies they could use to ride out the impending culling. Their plan was to emerge into the clean world and bring about the Fourth Reich. Of course, the Allies got wind of this, too, and made their own attempts to stop the Nazis throughout history. The OSS' and later the CIA's Department of Antiquities Verification, Investigation and Defense was one clandestine organization founded to root out the Nazi vaults, stop any further mystical acquisitions, and generally defend against future Nazi occult attacks. The KGB set up a similar organization, although theirs was a bit more bent on using what they found to tip the balance of the Cold War.

In the end, however, no one could avert the apocalypse, which came in the form of a meteorite that broke apart on reentry and vaporized London, Moscow, and Washington DC and blanketed the sky in dust. Several generations later, the dust has settled, nature has reclaimed the world, the Nazis have crawled out of their bunkers armed with technical expertise generally lost to Humanity. Nazi City-states have sprung up behind thick concrete walls and the wilds beyond are considered tainted and uncivilized. Within those walls, fascist regimes maintain a stranglehold on civilization.

I'll take off that tin foil hat now and discuss initial design goals. This is probably a bit gonzo, but hey, it's based on a Nazi conspiracy theory. It won't work if it's not as over the top as the premise, right? So I began by just listing things I thought would be interesting and fitting:

• Mutants!
• Occult Magic!
• Nazi UFOs!
• Weird Science!
• Wastelands!
• Crumbling Cities!
• Emergent City-States!
• Emergent Evil (Nazi) Empire!
• Biological Experimentation!

Looking at this list, it feels like a mix of After the End and Monster Hunters might make a fairly good fit. Mashing them together will take some work, and hopefully, I can stick with this long enough to see it through. If not, I will probably come back to it at a later date anyway. This is one of my three settings that gets periodic love (the other two being Starfall and Dark Horizons).

I plan on attacking this in the following way:

• Establish a Timeline to support future worldbuilding and guide rules development.
• Write up a brief description of The End as described in GURPS After the End - The New World. This will be crucial for developing appropriate templates later on.
• Develop a set of templates, most likely heavily based on those in After the End.
• Address what technology is readily available, what is rare, and just what the Nazis have.
• Sort out how magic and any powers work. This will likely be where I delve into Monster Hunters for inspiration.
• Make some sample PCs, run them through a couple of playtests, and see what works and what breaks.

So next installment will be comprised of a working timeline of events leading up to and through the start of the game.

Nymphs Part 3: Tree Nymph

The crystal clear water of the icy pool shimmered and rippled in the still air of the morning. Gradually, the ripples grew in an upward undulation that formed shapely calves, then thighs, and eventually a fully formed woman of surpassing beauty.

Nymphs are loci geniuses that inhabit various natural places. While similar to what are sometimes called “fae”, they more closely resemble elementals of a specific locale. They are inherently tied to the location they inhabit; indeed, their very existence depends on the wellbeing of the environment. And they defend it vehemently.

All nymphs exercise a measure of control over their homes and use this, in combination with their preternatural beauty to ward off attacks. Their beauty is terrible and captivating, and they use this mercilessly to their advantage.

As dangerous as nymphs can be, they are excellent sources of information on the area in which they dwell, and if befriended, they make powerful allies. However, their legendary shyness makes this difficult, and their sadistic impulses make it doubly dangerous!

Tree Nymph

CER 72 (OR 31 and PR 41)

Tree nymphs are spirits of place who watch over woodland areas.  They are closely attached to trees and may not stray more than a short distance from their home tree without becoming seriously ill.  They defend their homes fiercely, employing magic to animate the plants and trees around them, usually while hiding inside a tree.  Some tree nymphs are experienced mages, but most are simple forest guardians.  All command great knowledge about their environment.

ST: 8                                                       HP: 8                                                      Speed: 6.00

DX: 12                                                    Will: 10                                                  Ground Move: 6

IQ: 10                                                     Per: 11

HT: 12                                                    FP: 12                                                     SM: 0

Dodge: 9                                                Parry: 10 (Unarmed)                           DR: 3

Bow (14): 1d impaling. Acc 3. Range 120/160. Bulk -7.

Club (14): 1d-1 crushing. Reach 1.

Punch (14): 1d-2 crushing. Reach C.

Animated Environment: Tree nymphs can animate the environment around them to grapple (Binding or Telekinesis) intruders with ST 10 or strike at them (1d crushing or impaling) with branches.

Stunning Beauty: By striking even the slightest pose, anyone who sees her must make a Fright Check at -5 and roll on the Awe table.

Threshold Entity: This being doesn’t breathe, drink, eat, or sleep, is immune to metabolic hazards, and is either insubstantial and invisible or substantial and visible.

Woodwalk: A tree nymph can see and move through wood without hindrance.

Traits: Acute Hearing 1; Appearance (Beautiful; Universal); Berserk (9) (Special Trigger, harming the wilderness); Callous; Can Be Turned with True Faith; Curious (15); Dependency (Home Tree; Daily); Dislikes Loud Noises; Divine Curse (Keep to the letter of any promise); Fearlessness 2; Fragile (Combustible); Higher Purpose (Protect Home Tree); Impulsive (12); Night Vision 5; Obsession (Protect Trees); Odious Personal Habit -1 (Capricious); Sadism (15); Sense of Duty (Home Tree); Shyness (Mild); Silence 2 (Limited, In Woodlands Only); Terrain Adaptation (Jungle or Woodlands); Unaging; Vulnerability (Iron x2); Walk on Liquid (Specialized, Water).

Features: Affected as Spirit.

Skills: Area Knowledge (Local)-12; Axe/Mace-14; Bow-14; Brawling-14; Camouflage-12; Intimidation-17; Naturalist-12; Sex Appeal-12; Stealth-14 (18 in jungles and woodlands); Wrestling-14.

Notes: Most nymphs won't negotiate because they are too shy.  Those who do are amiable enough, but dealing with such an astounding beauty is often disconcerting – especially while under the effect of her intoxicating beauty (see above).  Always scars from wounds inflicted by iron.

Nymphs Part 2: Mountain Nymph

The crystal clear water of the icy pool shimmered and rippled in the still air of the morning. Gradually, the ripples grew in an upward undulation that formed shapely calves, then thighs, and eventually a fully formed woman of surpassing beauty.

Nymphs are loci geniuses that inhabit various natural places. While similar to what are sometimes called “fae”, they more closely resemble elementals of a specific locale. They are inherently tied to the location they inhabit; indeed, their very existence depends on the wellbeing of the environment. And they defend it vehemently.

All nymphs exercise a measure of control over their homes and use this, in combination with their preternatural beauty to ward off attacks. Their beauty is terrible and captivating, and they use this mercilessly to their advantage.

As dangerous as nymphs can be, they are excellent sources of information on the area in which they dwell, and if befriended, they make powerful allies. However, their legendary shyness makes this difficult, and their sadistic impulses make it doubly dangerous!

Mountain Nymph

CER 73 (OR 27 and PR 46)

Mountain nymphs are spirits of place who watch over mountainous areas.  They are closely attached to particular passes, grottos, peaks, etc., and may not stray more than a short distance from them without becoming seriously ill.  They defend their homes fiercely, employing magic to animate the mountain itself, often while dancing about high above.  All mountain nymphs command great knowledge about their environment.

ST: 9                                                       HP: 10                                                    Speed: 6.00

DX: 12                                                    Will: 10                                                  Ground Move: 6

IQ: 10                                                     Per: 11                                                   Climbing Move: 6

HT: 12                                                    FP: 12                                                     SM: 0

Dodge: 9                                                Parry: 10 (Unarmed)                           DR: 5

Punch (14): 1d-1 crushing. Reach C.

Quarterstaff (14): 1d+1 crushing (swing) or 1d crushing (thrust). Reach 1, 2*.

Animated Environment: Mountain nymphs can animate the environment around them to slide or knock intruders from their feet (target takes 3d crushing double knockback no wounding), strike at them (1d crushing or impaling) with rocks from above, or cause the ground to partially swallow a person – treat as Binding 10.

Difficult Terrain: A mountain nymph can cause anyone within their domain to have difficulty maintaining their balance or moving about.  The victim must roll a Quick Contest between his Will and the nymph's Will.  On a failure, the subject suffers a -2 penalty to DX and -2 penalty to Acrobatics, Jumping, Climbing, and Skiing lasting a number of minutes equal to his margin of failure.

Stunning Beauty: By striking even the slightest pose, anyone who sees her must make a Fright Check at -5 and roll on the Awe table.

Threshold Entity: This being doesn’t breathe, drink, eat, or sleep, is immune to metabolic hazards, and is either insubstantial and invisible or substantial and visible.

Traits: Acute Hearing 2; Appearance (Very Beautiful; Universal); Berserk (9) (Special Trigger, harming the wilderness); Callous; Can Be Turned by True Faith; Curious (15); Dependency (Home Mountain; Daily); Dislikes Loud Noises; Divine Curse (Keep to the letter of any promise); Fearlessness 2; Higher Purpose (Protect Home Mountain); Impulsive (12); Odious Personal Habit -1 (Capricious); Perfect Balance; Sadism (15); Sense of Duty (Home Mountain); Shyness (Mild); Super Jump 1; Terrain Adaptation (Mountain); Unaging; Vulnerability (Iron x2).

Features: Affected as Spirit.

Skills: Area Knowledge (Local)-12; Brawling-14; Climbing-16; Dancing-16; Intimidation-17; Jumping-16; Naturalist-12; Quarterstaff-14; Sex Appeal-12; Stealth-14.

Notes: Most nymphs won't negotiate because they are too shy.  Those who do are amiable enough, but dealing with such an astounding beauty is often disconcerting – especially while under the effect of her intoxicating beauty (see above).  Always scars from wounds inflicted by iron.

This Time It IS Rocket Science!

This time, I’m going to get into how I make rough apogee predictions for model rockets. Below is a derivation of the formulas necessary for predicting the apogee of a spherical bovine rocket undergoing air drag.

Warning: Math Ahead

So ultimately, we want to know how high the rocket will go. I am going to call this “y”, “displacement” or “apogee” interchangeably. I might even call it the height. Either way, this is what we are ultimately trying to solve for.

Anyone who has taken a basic calculus or physics class probably recognizes a few truths:

and

That is to say, the change in location of an object over a period of time is its velocity, and its change in velocity over a period of time is its acceleration. Thankfully, we can also say this in reverse:

and

This becomes important when we consider that the flight of any object is based on the sum of the forces acting on it. This is grounded in Newton’s Laws of Motion. Thus we know that the sum of our forces is

where F = force, m = mass, and a = acceleration. Thus,

Now we have a few terms here that we need to sort out: F_Thrust, F_Drag, and F_Weight. Of these, we can generally not worry about F_Thrust because that information is available based on our motor. Likewise, we know that F_Weight = mg, where g is the acceleration due to gravity. This leaves F_Drag for us to define:

where ρ = the density of air, C_D = the coefficient of drag, A = the crossectional area of the rocket, and v = the velocity. This may seem like a lot of information, but much of it really doesn’t change with time for our purposes here. So I am going to combine a bunch of these into a constant. I will do this a few more times to clean up equations and put them in more easily recognizable forms, too.

Now we have a simpler looking equation:

Substituting this and the formula for F_Weight, we get:

One more substitution, referring back to the beginning gives us

and we are ready to separate the variables and integrate.

But first, we are going to use some algebraic manipulations to get this looking like something we can integrate more easily:

Let

Thus

Now it’s time to integrate both sides:

Both m and k are constants, so we pull those out and integrate the right side:

We should now recognize the integral on the left as tanh^-1 u:

By the definition of tanh^-1, we can perform the following manipulations:

Therefore,

And define the constant

This lets us say:

Raising both sides to the e power gives:

Then we multiply both sides by the denominator:

Expanding the right side gives us:

Next, I need to isolate my v’s on one side:

Next, factor out v:

And divide both sides by (-e^xt-1):

Put more neatly:

And thankfully, we know that t = impulse divided by thrust, both of which are specifications provided by our motors. So now we know the final velocity when the motor finishes burning its fuel, but that doesn’t tell us either how high the rocket is at that point or how far it continues to coast. For that information, we need more integration.

We will begin by solving for y_Burn, or how far the rocket travels while the motor is still providing thrust. For simplicity’s sake, we will assume the rocket’s weight does not change during this time (we are launching a frictionless spherical cow, aren’t we?), so m will continue to refer to the mass of the rocket while it is full of propellant.

Referring back to our original equation, we know that:

So we can say

By separating the variables and integrating both sides, we get:

Which becomes:

Now we know the rocket’s altitude when the motor cuts out, but the rocket won’t instantly stop; it will continue to coast. So let y_Coast = the distance the rocket coasts on its momentum before beginning its descent. That is to say, how far will the rocket travel upward once F_Thrust = 0. Note that since the rocket has exhausted all of its fuel, we no longer use m_Full – we are now use m_Empty.

This should all look a bit familiar, but not that because F_Thrust = 0, that term is simply missing:

By integrating both sides, we get:

Which becomes:

Now, we know the rocket’s apogee will be the sum of how high it goes while under power (y_Burn) and how far it coasts before the acceleration due to gravity starts returning it to Earth (y_Coast):

And there you have it! To summarize:

Where,

A = the area of the rocket’s cross-section normal to its velocity vector.

C_D = the rocket’s coefficient of drag.

F_Thrust = the motor’s thrust in Newtons.

g = the acceleration due to gravity.

I = the motor’s impulse in seconds.

m_Empty = the mass of the rocket after burnout.

m_Full = the mass of the rocket at liftoff.

ρ = the density of air.

Of course, the astute reader will notice that through all of that mess, there is one term still undefined- C_D. This is the coefficient of drag, and determining it generally requires experimentation or running simulations. For my purposes, that is where OpenRocket and SolidWorks come in. Both are capable of determining C_D.

Did you survive? I warned you there’d be math!

It's Not Rocket Science!

Today's post was going to be a derivation of the formulas I used to predict a rocket's performance. It does get pretty math-intensive, and so I wrote it out ahead of time in word to more easily proof before pasting into here. This was a mistake. The formulas didn't transfer. Not only that, but I'm still looking for a good way to put them and any future math I may decide to include, in this blog. So instead of math, you're getting a llama.

Was this better than a few pages of integration?

Puissant Weapon (Sorcery)

Today's entry is a spell commonly used to enchant weapons:

Puissant Weapon

Key Words: Weapon Buff.

Full Cost: 17 points for level 1, 23 points for level 2, and 30 for level 3.

Casting Roll: None. Use Innate Attack (Gaze) to aim.

Range: 100 yards.

Duration: 3 minutes.

The enhanced weapon inflicts more damage for the duration. Add the spell’s level to the basic damage inflicted by the weapon (maximum 3). This stacks with mundane damage bonuses, like those from Committed or All-Out Attack (Strong) or quality bonuses, but not from magical sources.

Statistics: Affliction 1 (HT; Accessibility, Only on weapons, -20%; Advantage, Puissant, +65%; Fixed Duration, +0%; Increased 1/2D, 10x,+15%; No Signature, +20%; Sorcery, -15%) [22]. Additional levels add further levels of Puissant to the Advantage enhancement (+117.5%) [+12]. Notes: "Puissant" is Burning Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [0.7] + Crushing Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [0.7] + Cutting Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [1] + Huge Piercing Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [1.1] + Impaling Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [1.1] + Large Piercing Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [0.8] + Piercing Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [0.7] + Small Piercing Attack 1 (Accessibility, Only to augment damage inflicted, -35%; Magical, -10%) [0.4].

Energy Point Cost Table

	Energy Point Cost
Weapon Type	+1	+2	+3
Staff	6	9	11
Wand	7	10	12
Projectile	3	3	4
Weapon	8	11	14

Nymphs Part 1: Cave Nymph

The crystal clear water of the icy pool shimmered and rippled in the still air of the morning. Gradually, the ripples grew in an upward undulation that formed shapely calves, then thighs, and eventually a fully formed woman of surpassing beauty.

Nymphs are loci geniuses that inhabit various natural places. While similar to what are sometimes called “fae”, they more closely resemble elementals of a specific locale. They are inherently tied to the location they inhabit; indeed, their very existence depends on the wellbeing of the environment. And they defend it vehemently.

All nymphs exercise a measure of control over their homes and use this, in combination with their preternatural beauty to ward off attacks. Their beauty is terrible and captivating, and they use this mercilessly to their advantage.

As dangerous as nymphs can be, they are excellent sources of information on the area in which they dwell, and if befriended, they make powerful allies. However, their legendary shyness makes this difficult, and their sadistic impulses make it doubly dangerous!

Cave Nymph

CER 68 (OR 26 and PR 42)

Cave nymphs are spirits of place who watch over caves, mines, and other subterranean areas.  They are closely attached to caverns, cave systems, grottos, and mines, and may not stray very far from their home domain without becoming seriously ill.  They defend their homes fiercely, employing magic to animate the stalagmites, stalactites, and loose rocks, often while hiding within rocks themselves.  All cave nymphs have great knowledge of their home caves and cannot get lost in any labyrinthine environment.

ST: 8                                                       HP: 8                                                      Speed: 6.00

DX: 12                                                    Will: 10                                                  Ground Move: 6

IQ: 10                                                     Per: 11

HT: 12                                                    FP: 12                                                     SM: 0

Dodge: 9                                                Parry: 10 (Unarmed)                           DR: 3

Club (14): 1d-1 crushing. Reach 1.

Punch (14): 1d-2 crushing. Reach C.

Animated Environment: Cave nymphs can animate the environment around them to grapple (Binding or Telekinesis) intruders with ST 10 or strike at them (1d crushing or impaling) with falling rocks or stalactites.

Gloom: Cave nymphs can exude a thick darkness through which they can see perfectly – just like any other darkness.  It is thickest up to one yard from the nymph, imposing a -10 penalty to Vision, and decreases by 1 every additional yard from the nymph.

Illumination: Cave nymphs can glow with a gentle luminescence that sheds light as a torch.  This makes the nymph stand out in the darkness and can be turned on or off as a free action.

Stonewalk: A cave nymph can see and move through stone unhindered.

Stunning Beauty: By striking even the slightest pose, anyone who sees her must make a Fright Check at -5 and roll on the Awe table.

Threshold Entity: This being doesn’t breathe, drink, eat, or sleep, is immune to metabolic hazards, and is either insubstantial and invisible or substantial and visible.

Traits: Absolute Direction; Acute Hearing 1; Appearance (Very Beautiful; Universal); Berserk (9) (Special Trigger, harming the wilderness); Callous; Can Be Turned by True Faith; Curious (15); Darkvision; Dependency (Home Cave; Daily); Dislikes Loud Noises; Divine Curse (Keep to the letter of any promise); Fearlessness 2; Higher Purpose (Protect Home Cave); Impulsive (12); Odious Personal Habit -1 (Capricious); Sadism (15); Sense of Duty (Home Cave); Shyness (Mild); Terrain Adaptation (Uneven); Unaging; Vulnerability (Iron x2).

Features: Affected as Spirit.

Skills: Area Knowledge (Local)-12; Axe/Mace-14; Brawling-14; Intimidation-17; Naturalist-12; Sex Appeal-12; Stealth-16; Wrestling-14.

Notes: Most nymphs won't negotiate because they are too shy.  Those who do are amiable enough, but dealing with such an astounding beauty is often disconcerting – especially while under the effect of her intoxicating beauty (see above).  Always scars from wounds inflicted by iron.