How Long Would Scifi Space Travel Really Take?

[Spacescifi]

 

 

The interesting thing about scifi space travel is that it remains hard even with scifi tech, so long you allow propellant and gravity limits to still exist.

In a way it is kind of a good thing, only in that it prevents widespread easy RKV starship use.

My question is how long would travel take if I give the specification and dimensions of the Venturestar but upgraded it with a literal ton of antimatter safely stored with scifi inert material (so long they do not crash)?

Serious Upgrade: A jump drive. Get to anywhere in vacuum within 7 LY in a blink. Takes an hour to spool up the drive each time, so don't expect to jump instantly.

With my modifications both thrust and delta V increase dramatically.

 

Mission Profile: Visit an Earth-like world 65 LY away.

 

Timeframe: 65 hours of spooling up the jump drive is a given, but the real issue is orbital speed differences.

 

The destination planet has a 100 kilometer speed difference with our Earth and also is orbiting counterclockwise, while our Earth orbits clockwise but rotates counterclockwise.

 

The Challenge: How long will it take our heavily upgraded Venturestar to reach this new world once they are in the star system? Let's assume we jump 65 LY into the system and attempt to use our propellant abd antimatter to match speed with the 100 kilometer speed difference, then do one more jump into low planetary orbit. So that is a total of 67 houts spooling up,  plus however long it takes to match the speed difference via thrust.

How long would 1g take to match a 100 kilometer speed difference in orbital direction going opposite our starship's original orbit?

 

Why it matters: Plot events. Mission profiles are necessary, since even with antimatter one cannot go anywhere with impunity due to lack of propellant, plus TWR matters for landing anywhere. So some planets will simply be off limits forever if the orbital speed difference is too high... like for example 1000 kilometers per sec orbital speed difference. That may sound implausible but it is an example of a an Earth-like we would probably be unable to visit quickly even if we jumped into their system with antimatter powered rockets.

 

Discuss.

Capacity
Payload to LEO	20,000 kg[1] (45,000 lb)
Launch history
Status	Cancelled
Launch sites	Kennedy, LC-39A
Total launches	0
First stage - VentureStar
Engines	7 RS2200 Linear Aerospikes[1]
Thrust	3,010,000 lb[1] (13.39 MN)
Propellant

Propellant	LOX/LH2[1

 

 

 

Edited January 7, 2020 by Spacescifi

[Terwin]

What stops you from pooling up the jump drive while you are using your rocket engine?

1 hour of spool time is long enough to accelerate by 35kps at 1 g

If you are spooling 67 times for an hour each, you can accelerate at less than 1m/s/s  and still do all of your accelerating during your spool-up time.

 

Also, you forgot sling-shots.  Jump close to a planet/star and let it change your trajectory for you instead of burning fuel.

Not a lot of need for the anti-matter drives aside from launch/landing if you can use falling/sling-shots for other velocity changes.(a gas giant may be more comfortable than a star, but a few jumps that sling-shot you around a near-by large mass can easily change your vector dramatically, including speeding up/slowing down by the relative orbital velocity of the body you are using compared to your target).

It would take a long time, but this jump drive could also get you close enough to C that you cover 7 light years in only 1 subjective hour(ie recharge time) if you keep falling towards a black-hole only to jump backwards shortly before the tidal forces rip apart your vessel.(you would jump far enough that the next jump would also happen just before tidal forces became too much, and just keep repeating until your maximum jump of 7ly is not far enough away to let you charge up for your next jump before getting too close)

[Spacescifi]

31 minutes ago, Terwin said:

What stops you from pooling up the jump drive while you are using your rocket engine?

1 hour of spool time is long enough to accelerate by 35kps at 1 g

If you are spooling 67 times for an hour each, you can accelerate at less than 1m/s/s  and still do all of your accelerating during your spool-up time.

 

Also, you forgot sling-shots.  Jump close to a planet/star and let it change your trajectory for you instead of burning fuel.

Not a lot of need for the anti-matter drives aside from launch/landing if you can use falling/sling-shots for other velocity changes.(a gas giant may be more comfortable than a star, but a few jumps that sling-shot you around a near-by large mass can easily change your vector dramatically, including speeding up/slowing down by the relative orbital velocity of the body you are using compared to your target).

It would take a long time, but this jump drive could also get you close enough to C that you cover 7 light years in only 1 subjective hour(ie recharge time) if you keep falling towards a black-hole only to jump backwards shortly before the tidal forces rip apart your vessel.(you would jump far enough that the next jump would also happen just before tidal forces became too much, and just keep repeating until your maximum jump of 7ly is not far enough away to let you charge up for your next jump before getting too close)

 

Clever. There is nothing stopping you from accelerating along the way while you spool up the jump drive... although that requires information about the planet you're traveling to and not just jumping in blind like in Star Trek.

 

Question... would the crew feel ANY g-force while doing orbital gravity slingshots with engines off?

 

I tend to think no, but would they?

I mean the ISS experiences just enough g-force to keep them in a low orbit, but the crew does not feel any weight at all.

Edited January 7, 2020 by Spacescifi
Gravity slingshots

[Bill Phil]

Just now, Spacescifi said:

 

Clever. There is nothing stopping you from accelerating along the way while you spool up the jump drive... although that requires information about the planet you're traveling to and not just jumping in blind like in Star Trek.

 

Question... would the crew feel ANY g-force while doing orbital gravity slingshots with engines off?

 

I tend to think no, but would they?

I mean the ISS experiences just enough g-force to keep them in a low orbit, but the crew does not feel any weight at all.

In free fall no force is felt except tidal forces, which can be minimized.

As an answer to the OP:

100 km/s at 1g is about 10 thousand seconds. Or about 2.8 hours. 

[Spacescifi]

27 minutes ago, Bill Phil said:

In free fall no force is felt except tidal forces, which can be minimized.

As an answer to the OP:

100 km/s at 1g is about 10 thousand seconds. Or about 2.8 hours. 

 

Thanks. So that means even going as fast as we comfortably xan, it's a few hours even once reach the planet we want to reach. And some planets remain unreachable if the the speed difference is too high... unless we are willing to do several days or weeks worth, maybe even months worth of orbital slingshots via jumping around.

That is the time we would unkeash the the tether pods and do the rotating gravity thing so the crew will still be strong for when they finally make their descent planetside.

If reality applied to scifi taught me anything it's that one does not simply go anywhere in space.... they must arrive.

[Shpaget]

It takes exactly as long as the plot requires.

[KSK]

A couple of comments.

The jump-drive figures are inconsistent. If it requires 1 hour to spool up and can jump 7 light years a go, then surely it only takes 10 jumps to traverse 65 light years? In which case you'd be spending 10 hours spooling up rather than 65? Unless you meant 1 hour per light year spool time.

It would help to post some useful figures on VentureStar - the ones posted don't let you calculate much of anything, particularly since those linear aerospikes and H2/LOX  are presumably being replaced by your antimatter engine and some propellant?

More generally, I had a quick look on the Project Rho site and couldn't really find a suitable 'off-the-shelf' antimatter engine for this scenario. If you want a decent thrust-to-weight ratio - required for that 1g acceleration - then you're looking at some form of anti-matter-thermal rocket, with ISPs in the 1-2K range. That doesn't really seem to be enough here. A 2000s specific impulse certainly isn't anything to sneeze at but for a 100km/s delta-V change, you're looking at a mass fraction of about 0.0016. In other words, for a 100 ton spacecraft, all but 0.5 tons is propellant. That's very rough and ready but it gets the point across I think.

On the other end of the scale, there's the utterly insane Beam Core engine with a thrust to weight ratio of 102 and an ISP of over 10 million (not a typo). Which sounds like the kind of go-anywhere-do-anything engine that would laugh at a mere 100km/s delta-V change. Unfortunately, it has the slight (but awesome) disadvantage of annihilating about 50g/s of antimatter. I imagine that the mass of shielding and cooling systems needed to deal with that kind of energy output will laugh just as hard at that puny 102 thrust-to-weight ratio and I'm pretty sure the resulting spacecraft won't be pulling 1g.

Unfortunately that seems to be the general pattern for pure antimatter rockets. Awesome ISP or decent acceleration but not both.

 

Edited January 8, 2020 by KSK

[Spacescifi]

12 minutes ago, KSK said:

A couple of comments.

The jump-drive figures are inconsistent. If it requires 1 hour to spool up and can jump 7 light years a go, then surely it only takes 10 jumps to traverse 65 light years? In which case you'd be spending 10 hours spooling up rather than 65? Unless you meant 1 hour per light year spool time.

It would help to post some useful figures on VentureStar - the ones posted don't let you calculate much of anything, particularly since those linear aerospikes and H2/LOX  are presumably being replaced by your antimatter engine and some propellant?

More generally, I had a quick look on the Project Rho site and couldn't really find a suitable 'off-the-shelf' antimatter engine for this scenario. If you want a decent thrust-to-weight ratio - required for that 1g acceleration - then you're looking at some form of anti-matter-thermal rocket, with ISPs in the 1-2K range. That doesn't really seem to be enough here. A 2000s specific impulse certainly isn't anything to sneeze at but for a 100km/s delta-V change, you're looking at a mass fraction of about 0.0016. In other words, for a 100 ton spacecraft, all but 0.5 tons is propellant. That's very rough and ready but it gets the point across I think.

On the other end of the scale, there's the utterly insane Beam Core engine with a thrust to weight ratio of 102 and an ISP of over 10 million (not a typo). Which sounds like the kind of go-anywhere-do-anything engine that would laugh at a mere 100km/s delta-V change. Unfortunately, it has the slight (but awesome) disadvantage of annihilating about 50g/s of antimatter. I imagine that the mass of shielding and cooling systems needed to deal with that kind of energy output will laugh just as hard at that puny 102 thrust-to-weight ratio and I'm pretty sure the resulting spacecraft won't be pulling 1g.

Unfortunately that seems to be the general pattern for pure antimatter rockets. Awesome ISP or decent acceleration but not both.

 

 

Yea I fudged my calcs big time. You were right

 Seven LY per jump. So the jumping won't take as long as I thought.

 

But thanks for the other information too.

 

Given the restrictions that propellant (need moar mass) and mass (need more mass if you need to cool engine) put on having my cake and eating it too (high thrust along with high or indefinite ISP), I may as well just cheat and go the route of full-on cheating.

 

In other words... auto-shifting speed and trajectory to match whatever target you are are rendezvousing with, whether it's a planet or a ship.

 

From there on it's just simple newtonian mechanics at play, unless it's a planet in which case the vessel must spend propellant to make orbit or drop like a stone.

 

Still arguably less propellant spent than if I did not autoshift speed and trajectory to match the target upon jumping.

Edited January 8, 2020 by Spacescifi

[KSK]

Or go with @Terwin's slingshot ideas.

Alternatively you could have a ship with a separate lander (high thrust antimatter engines, gets your crew to the surface and back) and mothership (high ISP antimatter engines, gets the crew everywhere else). It may also be worth noting that 1g constant acceleration is really quite overpowered. Lifted directly from the Project Rho site:

"Consider a 1,000 ton spacecraft with a 10,000 km/s exhaust velocity and an acceleration of 0.722 m/s/s. For a 1 AU trip at constant acceleration, flipping at the midpoint, it will take 10.5 days and consume 66 tons of propellant/fuel."

It's stating the obvious but 0.7ms^-2 is only 0.07g (roughly) and still gives you a fairly impressive journey time for quite a reasonable quantity of propellant. 1g is nice for providing artificial gravity en-route but it's not required for decent journey times. I haven't looked it up but I suspect that a 0.07g acceleration and 10,000 km/s exhaust velocity is feasible with quite a few of the engines listed on Project Rho.

As for a lander - my apologies for sounding like a busted record - but here's another Project Rho snippet that might be of interest:

"The low mass ratio of antimatter rockets enables missions which are impossible using any other propulsion technique. For example, a reusable antimatter-powered vehicle using a single-stage-to-orbit has been designed [Pecchioli, 1988] with a dry mass of 11.3 tons, payload of 2.2 tons, and 22.5 tons of propellant, for a lift-off mass of 36 tons (mass ratio 2.7:1). This vehicle can put 2.2 tons of payload into GEO and bring back a similar 2.2 tons while using 10 milligrams of antimatter. Moving 5 tons of payload from low-Earth orbit to low Martian orbit with an 18-ton vehicle (mass ratio 3.6:1) requires only 4 milligrams of antimatter."

2.2 tons of payload is a bit puny for a standalone SSTO (although you can't complain about a 36 tons wet mass!) but it should be plenty for getting a few crew down to the surface and back from an orbiting mothership. The propellant is unspecified but water should be fine (I say this because several of the thermal-antimatter rockets described on the site use water) and is likely to be widely available and more convenient to obtain and store than hydrogen.

TL:DR - yes I think your VentureStar based single-stage-to-anywhere idea will require cheating. However, you could probably devise a fairly hard sci-fi alternative, where the only 'cheating' is your original jumpdrive concept without built-in velocity matching.

Personal opinion - if you must arrive, then arriving by jumping into the system, performing a daring slingshot maneuver to match velocity with your target planet and then using your awesome antimatter engines for final approach and orbit insertion is both pretty damn cool and lets you, the writer, get a bit of actual astrogation into your spaceflight story. Which is always nice to give it that hard sci-fi feel Plus it allows time for some other bits of storytelling, for example:

The crew are scanning their destination as they approach (maybe firing off a couple of probes in the process). Everything looks fine - until they light the engines for final approach just as one probe mysteriously vanishes...

The crew need to pull off a daring escape. They can do it - but only by using a recklessly brave slingshot maneuver which takes them dangerously close to [your celestial body of choice] to get every last m/s of delta-V from the Oberth effect...

 

Edited January 8, 2020 by KSK

[Spacescifi]

15 minutes ago, KSK said:

Or go with @Terwin's slingshot ideas.

Alternatively you could have a ship with a separate lander (high thrust antimatter engines, gets your crew to the surface and back) and mothership (high ISP antimatter engines, gets the crew everywhere else). It may also be worth noting that 1g constant acceleration is really quite overpowered. Lifted directly from the Project Rho site:

"Consider a 1,000 ton spacecraft with a 10,000 km/s exhaust velocity and an acceleration of 0.722 m/s/s. For a 1 AU trip at constant acceleration, flipping at the midpoint, it will take 10.5 days and consume 66 tons of propellant/fuel."

It's stating the obvious but 0.7ms^-2 is only 0.07g (roughly) and still gives you a fairly impressive journey time for quite a reasonable quantity of propellant. 1g is nice for providing artificial gravity en-route but it's not required for decent journey times. I haven't looked it up but I suspect that a 0.07g acceleration and 10,000 km/s exhaust velocity is feasible with quite a few of the engines listed on Project Rho.

As for a lander - my apologies for sounding like a busted record - but here's another Project Rho snippet that might be of interest:

"The low mass ratio of antimatter rockets enables missions which are impossible using any other propulsion technique. For example, a reusable antimatter-powered vehicle using a single-stage-to-orbit has been designed [Pecchioli, 1988] with a dry mass of 11.3 tons, payload of 2.2 tons, and 22.5 tons of propellant, for a lift-off mass of 36 tons (mass ratio 2.7:1). This vehicle can put 2.2 tons of payload into GEO and bring back a similar 2.2 tons while using 10 milligrams of antimatter. Moving 5 tons of payload from low-Earth orbit to low Martian orbit with an 18-ton vehicle (mass ratio 3.6:1) requires only 4 milligrams of antimatter."

2.2 tons of payload is a bit puny for a standalone SSTO (although you can't complain about a 36 tons wet mass!) but it should be plenty for getting a few crew down to the surface and back from an orbiting mothership. The propellant is unspecified but water should be fine (I say this because several of the thermal-antimatter rockets described on the site use water) and is likely to be widely available and more convenient to obtain and store than hydrogen.

TL:DR - yes I think your VentureStar based single-stage-to-anywhere idea will require cheating. However, you could probably devise a fairly hard sci-fi alternative, where the only 'cheating' is your original jumpdrive concept without built-in velocity matching. Personal opinion - if you must arrive, then jumping into the system, performing a daring slingshot maneuver to match velocity with your target planet and then using your awesome antimatter engines for final approach and orbit insertion is both pretty damn cool and lets you, the writer, get a bit of actual astrogation into your spaceflight story. Which is always nice to give it that hard sci-fi feel .

 

 

 

I like the concept of orbital slingshots, but I have a ferling it would take a long time.

 

How much time would it take to match 100 kilometer per second speed difference using gravity slingshots?

 

I know it depends on the planet used for the slingshot, so let's say there just so happens to be a Jupiter size gas giant in the system (how convinient), how long would it take to change my speed doing that?

[KSK]

Not a clue (although this page might help if you want to crunch the numbers yourself) but I can think of a couple of comparisons.

The Apollo spacecraft were travelling at approximately 1km/s as they entered the Moon's sphere of influence. Therefore looping around the Moon on a free return trajectory would be a rather extreme slingshot maneuver, adding at least 1km/s of delta V (to get the spacecraft turned around) and in practice quite a bit more (to get the spacecraft heading back towards Earth). Unsure of the exact numbers. Time from sphere of influence entry to lunar orbit insertion (LOI) burn was about 12 hours.

So the Moon's gravitational field is enough for low single-digit km/s delta-V changes over a day.

More impressively, Voyager II picked up around 18km/s from its Jupiter flyby. No idea about times.

But yes, relying on slingshots alone would probably take quite a bit of time. Using slingshots and engines would take rather less of course (remember that 0.07g drive taking 10 days to travel 1 AU? That's spending half the journey braking. Accelerating at 0.07g for 5 days gets you about 300 km/s delta-V (assuming my maths is right. It's getting late here so it may not be ) and travelling at 300km/s would get you from Earth to Jupiter in a month. Assuming you didn't plan on stopping at Jupiter.

So, very roughly speaking, you're looking at weeks to months of travel time to get around a star system. Using your jump drive, you could scout out the Alpha Centauri system and get back to Earth, in a handful of months. That's not Star Trek journey times by any means but it's still pretty impressive and can be done in a much harder sci-fi setting than Star Trek (admittedly, not a high bar to clear.)

What's the big hurry anyway? Here we're talking about interstellar journeys in a very small fraction of a human lifetime. More to the point for a sci-fi setting, you could have 'interstellar mail ships' delivering communications between planets in a reasonable timeframe for those planets to interact with each other in a meaningful manner. You could have an interstellar civilization held together by the interstellar equivalent of the old Pony Express! Loads of story telling potential there. To my mind it would also strike an interesting balance between 'space is routine' and 'space is hard' which seems to be something you've been looking for?

 

Edited January 8, 2020 by KSK

[Guest]

For intrasystem travel, try this:
http://www.projectrho.com/public_html/rocket/supplement/TransitNomogram03b.pdf
If you can use antimatter, then it's safe to assume you can afford a skew-flip trajectory. This nomogram applies to this case. This will literally tell you everything, if you've got any two numbers. 

[Terwin]

20 hours ago, KSK said:

So the Moon's gravitational field is enough for low single-digit km/s delta-V changes over a day.

More impressively, Voyager II picked up around 18km/s from its Jupiter flyby. No idea about times.

But yes, relying on slingshots alone would probably take quite a bit of time. Using slingshots and engines would take rather less of course (remember that 0.07g drive taking 10 days to travel 1 AU? That's spending half the journey braking. Accelerating at 0.07g for 5 days gets you about 300 km/s delta-V (assuming my maths is right. It's getting late here so it may not be ) and travelling at 300km/s would get you from Earth to Jupiter in a month. Assuming you didn't plan on stopping at Jupiter.

So, very roughly speaking, you're looking at weeks to months of travel time to get around a star system. Using your jump drive, you could scout out the Alpha Centauri system and get back to Earth, in a handful of months. That's not Star Trek journey times by any means but it's still pretty impressive and can be done in a much harder sci-fi setting than Star Trek (admittedly, not a high bar to clear.)

Why would it take very long?  Most of the change in velocity takes place during the brief time when the vessel is closest to the body in question, and you can teleport every hour, so just do the most effective hour each jump and be done in hours or perhaps days.

The space station orbits the earth every 90 minutes, so you could presumably manage 2/3 of an orbit each hour/jump, probably a bit more as you will likely be moving faster than orbital velocity.

The 'u-turn' of the slingshot looks like ~1/2 of an orbit, so it looks like you could probably manage the majority of a slingshot maneuver each jump/hour, so long as you are above the orbital velocity of the body you are using to turn/slow down(if not, you might just do a 'falling' type trajectory: falling towards and jumping just before hitting the atmosphere to speed up, or appearing just above the atmosphere and let gravity slow you down if slowing down).

So, using the moon you could probably manage 100km/s in less than 200 hours(0.5 km/s each jump due to assuming only half the benefit of the sling-shot for the sake of being conservative, 8.3 days), and using Jupiter, you could probably manage it in less than half a day(100/9 is just over 11), although you may need good radiation shielding.

(presumably the sun would work even better, but you may not be set up to handle the radiation/heat-load that would entail)

[KSK]

Well you still need to travel from your slingshot to your destination which will take some time but yes - good point. Was forgetting about the teleport-and-repeat trick.

[Terwin]

7 minutes ago, KSK said:

Well you still need to travel from your slingshot to your destination which will take some time but yes - good point. Was forgetting about the teleport-and-repeat trick.

Yep, add one extra hour for the last jump, I was just giving an estimate of the time to velocity-match.

[Spacescifi]

On 1/9/2020 at 10:13 AM, Terwin said:

Why would it take very long?  Most of the change in velocity takes place during the brief time when the vessel is closest to the body in question, and you can teleport every hour, so just do the most effective hour each jump and be done in hours or perhaps days.

The space station orbits the earth every 90 minutes, so you could presumably manage 2/3 of an orbit each hour/jump, probably a bit more as you will likely be moving faster than orbital velocity.

The 'u-turn' of the slingshot looks like ~1/2 of an orbit, so it looks like you could probably manage the majority of a slingshot maneuver each jump/hour, so long as you are above the orbital velocity of the body you are using to turn/slow down(if not, you might just do a 'falling' type trajectory: falling towards and jumping just before hitting the atmosphere to speed up, or appearing just above the atmosphere and let gravity slow you down if slowing down).

So, using the moon you could probably manage 100km/s in less than 200 hours(0.5 km/s each jump due to assuming only half the benefit of the sling-shot for the sake of being conservative, 8.3 days), and using Jupiter, you could probably manage it in less than half a day(100/9 is just over 11), although you may need good radiation shielding.

(presumably the sun would work even better, but you may not be set up to handle the radiation/heat-load that would entail)

 

I do not presume to understand orbital motions as well as some, but correct me if I get this wrong:

 

Wanna increase your speed? Fly toward a planet that is flying away from you. Flying close adds to your forward speed, although you will likely be in excess of escape velocity anyway. Which is why repeated TP is needed... it's the only way you can keep doing gravity assisted flyby's without burning propellant.

 

Wanna slow your forward motion? Fly toward a planet flying toward you. Your speed will reduce on each flyby until you reach low orbit speed. From there the only way to further slow is via aerocapture (fiery atmosphetic reentry). 

If you are trying to land on an airless moon, you are better off using another bigger world to get your speed adjusted before going there via teleport.

No matter what some propellant will be expended hor airless moon landings.

[Terwin]

On 1/12/2020 at 12:10 AM, Spacescifi said:

 

I do not presume to understand orbital motions as well as some, but correct me if I get this wrong:

 

Wanna increase your speed? Fly toward a planet that is flying away from you. Flying close adds to your forward speed, although you will likely be in excess of escape velocity anyway. Which is why repeated TP is needed... it's the only way you can keep doing gravity assisted flyby's without burning propellant.

 

Wanna slow your forward motion? Fly toward a planet flying toward you. Your speed will reduce on each flyby until you reach low orbit speed. From there the only way to further slow is via aerocapture (fiery atmosphetic reentry). 

If you are trying to land on an airless moon, you are better off using another bigger world to get your speed adjusted before going there via teleport.

No matter what some propellant will be expended hor airless moon landings.

Assuming 'flying towards' is referring to the starting point of a sling-shot, that sounds about right, but in either case the sling-shot is not the only option,  you can also use gravity directly to accelerate or decelerate to a velocity very close to a relative stop compared to your target.  (appear close the the body with your velocity moving away would slow you down, while appearing ~ 1 hour away form the body but falling towards it to speed up; works better with a deeper gravity well).

With accurate enough math and measurements you could theoretically teleport to several inches above the surface with a relative velocity of only a few cm per second, but that seems higher risk than having some means of slowing down and appearing a few hundred meters above the surface.

If you have incredibly accurate/reliable sensors and teleportation, you don't need any other fuel/engine.

[PositronLance001]

On 1/7/2020 at 4:01 PM, Spacescifi said:

Clever. There is nothing stopping you from accelerating along the way while you spool up the jump drive... although that requires information about the planet you're traveling to and not just jumping in blind like in Star Trek.

Except time dilation.  But that only matters at extreme travel times.