Helmet field testing? CdA impact

[Osiris]

I did some field testing of my own this morning, comparing the results of three of my helmets: the Specialized Evade, LG Vortice, and SH+ Eolus.

Aerodynamic efficiency was the only thing I wanted to know, so I drove out to the backside of Sugarloaf hill. The front side is steeper and longer, but I'm not interested in knowing how helmets perform at speeds exceeding 40 mph, nor was I prepared to repeat the climb to the top of Sugarloaf 15 times on a broiling hot day in July. The backside is ideal because it's sloped just enough to achieve speeds of 35+ mph when coasting down on my Specialized Venge, and the climb back to the top isn't nearly as demanding.

I had planned to do the tests in groups of five for each helmet, but I seem to have miscounted and did six runs with the Specialized Evade. No matter; more data can't be a bad thing. Each test was performed with my hands in the drops, starting at the very top with a rolling speed of ~5 mph, and then just coasting all the way down.

Below are the top speeds achieved with each helmet:

Specialized Evade
34.0 mph, 35.6 mph, 35.1 mph, 35.3 mph, 34.2 mph, 36.9 mph. Average: 35.18 mph

SH+ Eolus
37.1 mph, 36.7 mph, 37.4 mph, 36.5 mph, 36.9 mph. Average: 36.92 mph

LG Vortice
36.9 mph, 36.9 mph, 37.4 mph, 36.7 mph, 37.4 mph. Average: 37.06 mph

As I suspected, a road helmet just doesn't belong in this sort of company. Even at 27 mph, I already experienced a lot of wind resistance and noise, and by the time I hit the top speed of 35 mph, it felt as if it had a parachute attached to it. It's only saving grace is the amount of cooling afforded by all those openings in the top and sides, but you pay for that with the enormous turbulence they create.

The surprise was the SH+ Eolus. It's better ventilated than the LG Vortice and leaves the rider's ears uncovered, but it doesn't give up much to the Vortice in aerodynamic efficiency. At the slower speeds I normally travel on my bents (~24-26 mph), the difference in efficiency between the Eolus and Vortice might not even be noticeable. However, on long rides you'd want better ventilation, and the Vortice would be a very poor choice except in colder weather. On a typical Florida Summer day, wearing the Vortice for long periods might prove fatal.

I should mention that the Vortice might not even be usable on a bent due to clearance issues with the rear tire (in the case of my M1) and getting it to fit whatever headrest you're using. It might be possible to modify the helmet for use on a bent though, and this is something I'm going to investigate.

 

[ed72]

I have an evade, it is slow on the bent too. I did not save the CdA figures but it led me to the Bell Star and it was good for general riding but I broke two of them (the vent covers slide closed, the mechanism breaks)

I know that stretch of road.

I never tested my TT helmet with the tail (Bell something or another) because there is a forum somewhere that said these types of helmets are slow on bents.

I think your testing approach is reasonable. It is similar to how I test tires. I have a hill where I coast from a standstill in a fixed position on a windless day and topspeed is 10-11 mph usually and then I just glide until the bike stops (can't do that on a bent). I run tires three times. I mark where they stop. Believe it or not some brand new tires are duds. The relative order aligns with the drum testing results but some tires don't do quite as well on my somewhat bumpy country roads (chippy). The difference between the LG and other helmet is not statistically significant, you could repeat the test and the results could be reversed but the Specialized would still be the dog of the test

 

[Osiris]

I know that stretch of road.

If you were on it before they resurfaced it, you should try it now. Smooth as a billiard table. Unfortunately the ride to the top isn't any easier. Ideally I would have done 10 test runs for each helmet, but after climbing that hill 17 times in a row, I just didn't have the energy.

I never tested my TT helmet with the tail (Bell something or another) because there is a forum somewhere that said these types of helmets are slow on bents.

We'll have to see. I just performed a bit of surgery to get the Vortice to fit over the M5's headrest, so now I just need to find a suitable hill to test it on. The front and back of Sugarloaf are too steep for a fast recumbent, but there are several roads in the area with more gentle slopes. I need to keep the speed realistic, so no descents at 70 mph! The amount of drag at 27 mph is already horrendous. I never noticed it before, probably because I'm concentrating on many other things, but at 27 mph, my normally tight fitting race cut jersey started fluttering a bit around the waist and shoulders. At 35 mph, it felt like the wind was going to tear the jersey right off me. When you're not doing anything but coasting, you really become aware of just how severe the effects of wind resistance are, and how much leg power it must take to overcome it.

I think your testing approach is reasonable. It is similar to how I test tires. I have a hill where I coast from a standstill in a fixed position on a windless day and topspeed is 10-11 mph usually and then I just glide until the bike stops (can't do that on a bent). I run tires three times. I mark where they stop.

I did that as well, although it was not part of my test. It just happened to be the case that I'd roll to a stop near the same mailbox each time, so I started keeping track of how close to the mailbox I got for each run. Oddly enough, I ended up in almost the same place each time, give or take about 10 feet, despite the differences in top speed.

The difference between the LG and other helmet is not statistically significant, you could repeat the test and the results could be reversed but the Specialized would still be the dog of the test

I'll be wearing my SH+ Eolus helmet on tomorrow's ride. If I can survive the heat with it on, then I'm going to permanently retire the Specialized helmet. I can't bear the thought of having that slug slowing me down any longer. It's got to go!

 

[ed72]

I did that as well, although it was not part of my test. It just happened to be the case that I'd roll to a stop near the same mailbox each time, so I started keeping track of how close to the mailbox I got for each run. Oddly enough, I ended up in almost the same place each time, give or take about 10 feet, despite the differences in top speed.

Same here. +/- 10 feet for one set of tires. Corsa Speeds were always about 30-50 feet beyond the Continental Supersonics with latex tubes but both of those were light years ahead of Schwalbe Pro Ones tubeless or any of the various Compass Ultra Legere tires...the Compass tires were equal to my high end 28 mm width tubulars. Third fastest were always Contin GP4000 28 mm with latex tubes. And yes, the difference between butyl tubes and latex was statistically measurable on my test road. I don't test any more because I can't hold a position and coast to a stop anymore and I am limited on tires anyway (width). Back then I wondered if these results had any bearing on rear world conditions. Over multiple weeks, I did Strava segment testing. Speeds using the Supersonics or Speeds got me KoMs on flats 2 mile stretches using my upright bike with aerobars but putting on the more normal tires (Pro Ones or GP40000) wouldn't get me close to the top 10 albeit these are on routes with many cyclists, so, 20 seconds lost is a lot.

I did a 50 mile training segment yesterday in 2:06 on 160 ish watts....regular kit. Perfect conditions 82-85F and terrible humidity. I was in zone 2. One road jumps to get on my wheel, which I do not like, so I slowly dialed it up to the low 30's to dump him but otherwise just 24-26 mph on the flats and tried to keep 19 mph on the hills. I think I'm going to try a 100 miles and if I can do under 4:10 in training on public roads, I might consider going to the velodrome to see if sub 4 hours is possible for me. If I had a Magic bike but I wonder if I could ride it, maybe sub 4 hours...in theory. 40 minutes in the pain cave is easy, 4 hours? In theory I have the power to do it. I can't do 10-15 hour training rides anymore, so, such an effort would be somewhat helpful preparation for PBP whether I succeed or not, who cares. Most of my hard riding has been in the hills, time for some long tempo rides.

WRT to topspeed testing. Not sure if it is valid or not but your approach seems like a sensibily quick way to test for gross improvements, especially on a hill like that. I found for instance that my topspeed on my Chung halfpipe could go from 37.xx to 38.xx just pulling my shoulders and tucking my neck. I did 5 replicates and it was consistent. If I tried this on a hill with a topspeed of only 20-25 mph, I doubt the improvement would be so obvious and then real math would be needed.

The rearward helmet strap. If adjusted to cover the upper ear, it pulls the ear back and flat. Free speed. None of that matters at 20 mph but at 30-35, it matters. Strap must be snug not flapping.

Wednesday forecast is for low winds (2 mph max)......I need to do some testing before I take off the fast front fork, I am going back to the stock but curious the cda effect

 

[Osiris]

Believe it or not, there's a local time trialist who did a 100 mile TT on his trainer. He filmed the whole thing, saying it was the worst experience he's ever had. A century at maximum effort is far too much torture for me, but 20 and 40K TT's sound doable. The hard part is going to be finding a stretch or road or trail safe enough to do them on. I'm told there's one called the Van Fleet trail which is 20 miles one way, but it's a bit of a drive for me to get there.

I see that Dave Brillhart uploaded a ride on Strava which he dubbed, "200W for 200KM".

https://www.strava.com/activities/1943685014#48993084181

If I could duplicate that on the M1, it would mean averaging ~27 mph for 124 miles, which would be quite an accomplishment.

Achieving a nearly 2 mph increase in speed by just swapping helmets still amazes me. I can't think of any other equipment swap that would make as great a difference. I still find it odd that the aerodynamic edge that the LG Vortice helmet has over the SH+ Eole is so marginal. Apparently those golf ball dimples, teardrop tail section, and other aero effects don't pay big dividends in terms of aerodynamic efficiency. Still, a 0.12 mph increase in speed can't simply be dismissed, especially as the miles pile up.

 

[ed72]

I see that Dave Brillhart uploaded a ride on Strava which he dubbed, "200W for 200KM".

Dave has an FTP of about 280 watts, so, 72% is 200 watts. Hard but very doable. I did a 200k down in Florida in 2015 or 2016 in like 6:30 hours at 221 watts NP off an FTP of 265-270 although it got hard at the end when Keith S and Mike K went off trying for a fast time leaving me for my lonesome but they were just having some fun. This was pretty much balls to the walls riding for me mid winter coming down from the north. When I see exorcist physiologists claiming 91-92% of FTP is possible for 5 or 6 hours, I ask to see the data of someone who actually did that. I have searched the Spring classics of the professionals, various world record rides, and long TdF breakaways. 200 watts is at the top of Dave's zone 2, I am sure it took concentration but it wasn't killer for him, I suspect. Several years ago, I had an endurance coach who was working me up to 10 hour rides at Tempo. He wanted me to eventually ride at 230-250 watts for ten hours. I got 6 hours at 230 watts eventually but then the power just wilted away as time increased. For whatever reason, I find muscular fatigue builds quicker on a bent than on an upright. Of course, Dave is a beast. I hear his wife is married. LOL.

I do think 90-92% (not 96% as some claim is achievable) of FTP is possible for 3 hours. I am not sure how fast this would be on a track because the surface rolling resistance is different.

The true long distance riders like the RAAM racers do 24 hour Strava events in the winter. I would poke my eyeballs out.

I must say I was a little surprised by the magnitude of speed difference on the Evade but not so surprised that it brought up the rear. On a bent, I think the sides catch a lot of wind. Not sure but it wasn't fast for me either. I try not to get hung up on absolute values. If I repeat something many times and it is always slower, it is slower. If it is slow and uncomfortable, it goes into the bin.

 

[Osiris]

Dave has an FTP of about 280 watts, so, 72% is 200 watts. Hard but very doable. I did a 200k down in Florida in 2015 or 2016 in like 6:30 hours at 221 watts NP off an FTP of 265-270 although it got hard at the end when Keith S and Mike K went off trying for a fast time leaving me for my lonesome but they were just having some fun. This was pretty much balls to the walls riding for me mid winter coming down from the north. When I see exorcist physiologists claiming 91-92% of FTP is possible for 5 or 6 hours, I ask to see the data of someone who actually did that. I have searched the Spring classics of the professionals, various world record rides, and long TdF breakaways. 200 watts is at the top of Dave's zone 2, I am sure it took concentration but it wasn't killer for him, I suspect. Several years ago, I had an endurance coach who was working me up to 10 hour rides at Tempo. He wanted me to eventually ride at 230-250 watts for ten hours. I got 6 hours at 230 watts eventually but then the power just wilted away as time increased. For whatever reason, I find muscular fatigue builds quicker on a bent than on an upright. Of course, Dave is a beast. I hear his wife is married. LOL.

Dave has tremendous endurance and a capacity to withstand pain the likes of which I've rarely seen in other individuals. In the old days when we rode together, he would always want to keep going, even when everyone else in the group was ready to call it quits. It wasn't long before we started finding excuses not to join any of his rides!

I would love to do a 200k on the M1 or M5, but my hip joints start to ache after about mile 50, and the harder I ride, the worse it gets. It's not a muscle ache or connective tissue soreness, but it's completely gone after a long rest, and it only happens when I ride a bent, never an upright. I once did a 106 mile ride on the M5, but I deliberately kept the effort very low (~18 mph) so that the joint pain would be mild enough for me to make it all the way, but it was no fun going that slow. I think my limit, if I were going at a decent speed on a bent, might be about 20-30 miles. It's something I intend to find out, but it will have to wait for colder weather. Maybe by then I'll have figured out how to wear the TT helmet on my M1.

 

[Osiris]

I just saw a deal I couldn't pass up: a brand new SH+ Eolus track helmet, normally selling for $359.99, on sale for $180! https://www.gizmocycling.com/SH-Eolus-White-p/60-0401.htm

The newer model looks even more aero than my current Eolus: the rider's ears are now fully enclosed and the drag inducing protrusions on the old version have been removed for a smoother shape. The downward curvature of the visor seems greater, hopefully leading to improved air flow with the rider's head tilted back, which was my only complaint about the old model.

 

[ed72]

The downward curvature of the visor seems greater, hopefully leading to improved air flow with the rider's head tilted back

Probably right there.

I think my medium sized Vanquish is faster than the large (have to prove it with data) because the visor sort of mashes into my cheek on the medium whereas there is a clear gap on the large to the extent cycling glasses just fit under there.

 

[Osiris]

Probably right there.

I think my medium sized Vanquish is faster than the large (have to prove it with data) because the visor sort of mashes into my cheek on the medium whereas there is a clear gap on the large to the extent cycling glasses just fit under there.

Speaking of helmet size, it's odd how large in diameter TT helmets are compared to my track and road helmets. I would think that the larger the helmet, the more drag it creates, no?

I just checked the current records at the Van Fleet trail, which is the only trail I know long enough to do a proper 40k TT on. It's 30 miles in one direction (10 miles longer than I thought). The fastest time Southbound was set by John Stautinger back in 2015, with an average speed of 25.5 mph. John also holds the "Out and Back" record, with an average speed of 23.5 mph. Looking at his upload, you can see how dramatically his speed dropped on the return ride, having apparently spent all his energy on the Southbound segment: https://www.strava.com/activities/452861605/segments/10882896647

I think that would be the perfect test for my new helmet and take both KOM's.

 

[ed72]

I think that would be the perfect test for my new helmet and take both KOM's.

There are few intersections and most are more like driveways although Green Pond Road is a dangerous one....BE CAREFUL on that ONE!!! I've never ridden it real hard, only on brevets and the like. Usually at 22-23 mph although on an upright I think Keith S. and I did it at about 25 mph, I never downloaded the file but we were hauling (at 100 miles into a 200k on upright bikes). Traffic (bikes) can be high down near the park towards Polk City. Just before the park, the trail surface is a bit bumpy but overall, the surface is pretty good. The northern part has never had traffic in my experience. I used to have a townhouse rental near there and road it a couple times per week casually on an upright. The trail is also fairly well sheltered from the wind.

 

[Osiris]

There are few intersections and most are more like driveways although Green Pond Road is a dangerous one....BE CAREFUL on that ONE!!! I've never ridden it real hard, only on brevets and the like. Usually at 22-23 mph although on an upright I think Keith S. and I did it at about 25 mph, I never downloaded the file but we were hauling (at 100 miles into a 200k on upright bikes). Traffic (bikes) can be high down near the park towards Polk City. Just before the park, the trail surface is a bit bumpy but overall, the surface is pretty good. The northern part has never had traffic in my experience. I used to have a townhouse rental near there and road it a couple times per week casually on an upright. The trail is also fairly well sheltered from the wind.

I've been thinking about how to plan the ride. It's about 58 miles round trip KOM, so doing that kind of distance in the scorching Summer heat sounds like a bad idea. The M1 is by far my fastest recumbent, but the seat becomes excruciating after 30 miles. I don't see how I could survive 58 miles on it, so I'll have to take the M5. I'll be doing it some time in the Fall or Winter. When it's cold, I don't run out of energy as quickly and probably won't need more than one water bottle, which is all I have room for on the M5. The record stands at 2:28:00 @ 23.5 mph, which is an average speed I can beat easily for the first half. Not sure what will happen after mile 40 though, because that's when my hip joints really start to hurt. It may be one of those cases where the pain just levels off at a certain point and I can push through it for the remaining 20 miles. I want to be sure, so as dull as it sounds, maybe I'll just go back and forth on my favorite trail until I reach the target mileage. It beats spending 2.5 hours on the trainer.

 

[ed72]

I've been thinking about how to plan the ride. It's about 58 miles round trip KOM, so doing that kind of distance in the scorching Summer heat sounds like a bad idea.

For me....I find 75-85F with high humidity to be a good balance of speed vs cooling. Like start at 75F before it gets warm expecting it to warm up. Very early start to avoid those crazy old guys on trikes riding 3 abreast at 6 mph. What is that November weather down there?

I did 35-40 miles in the hills today with 2500-3000 feet of climbing, it was 82-88F. The climbs were a bit hot. I was planning on 55 miles but forgot my ice cream money and then my rear disk wheel cover assploded. So, I called it a day.

 

[Osiris]

For me....I find 75-85F with high humidity to be a good balance of speed vs cooling. Like start at 75F before it gets warm expecting it to warm up. Very early start to avoid those crazy old guys on trikes riding 3 abreast at 6 mph. What is that November weather down there?

I'd forgotten about those guys on trikes -- the "CRABS", as they call themselves. I hear they can become rather belligerent, so I'd better carry my pepper spray.

November temps here can be pretty low early in the morning, but things heat up rapidly, so it often doesn't pay to dress warmly. My Winter clothing would only create more drag, anyway. Now that I've had more time to think about it, I may just do the North-South segment separately, which is the one with the fastest KOM (25.5 mph). That way I can bring the M1 and add 1-2 mph to my average speed. If I rest a bit after reaching the South end, I may decide to take the Northbound KOM as well, where the average speed I'll have to beat is slower (24.4 mph). I'd love to know what it is about the M1's seat that's causing so much soreness in my lower back and hip area. If it were not for that, I could ride it the whole 58 miles without resting and claim all three KOM's at once.

I did 35-40 miles in the hills today with 2500-3000 feet of climbing, it was 82-88F. The climbs were a bit hot. I was planning on 55 miles but forgot my ice cream money and then my rear disk wheel cover assploded. So, I called it a day.

Wow, was that the FLO disk wheel?

 

[Osiris]

So I did another "field test" this morning, wearing the SH+ Eolus helmet in place of my usual Specialized Evade road helmet. The Eolus has an enormous advantage at very high speeds (35 mph+), but I wanted to see whether it would confer any noticeable performance advantage at speeds I can reach under my own power. Now there's a straight section of trail that's about a third of a mile long, which I've often used as my sprint zone. It starts and ends with an abrupt right turn, so you can't get a running start, and you need to slow down in time to make the sharp right at the end, so there's really very little space to work with. I've been doing mini-sprints on that section of trail for years on my uprights, and though I have occasionally exceeded 28 mph, never once have I managed to hit a top speed of 29 mph. This morning I hit 30 mph. There was no wind out there to help me, and I wasn't feeling particularly strong, having already done two hard efforts before I even got there. The only thing I can attribute it to is the helmet. I'll try it a few more times, and if I manage to hit 30 mph consistently, then there will be no doubt.

 

[DavidCH]

SH+ Eolus helmet

Yes... sure looks aero but how heavy and how hot is it to wear?

 

[Osiris]

Yes... sure looks aero but how heavy and how hot is it to wear?

Surprisingly it's not much heavier than my road bike helmet. The relative lack of ventilation however is a potential problem, especially in a place as hot as Florida. So far I've done several rides wearing it when temperatures hovered in the mid 90F's with high humidity. I didn't experience any discomfort, but I noticed that there was more sweat in my hair than usual when I took the helmet off after a 2.5 hour ride.

I did two more test sprints this morning, and the results were nearly as good as yesterday with my top speed exceeding 29 mph both times. My power output was a bit down from yesterday, else I'm sure I would have hit 30 mph again. There's no doubt now that the helmet alone is worth an extra 1-2 mph at high speeds. It occurred to me on the drive back that I might have been able to squeeze even more speed out of the Eolus by keeping my head as low as possible so as to minimize my frontal profile:

This isn't feasible with a conventional road bike helmet because their overall shape and ventilation openings are designed to be aerodynamically efficient only when they're facing directly into the wind. If the rider tips his head down to minimize his frontal profile, the wind will hit the top of the helmet instead of the front, creating a lot of drag:

 

[ed72]

Wow, was that the FLO disk wheel?

No, I used a PowerTap G3 hub as a power meter laced to a conventional rim covered by an aerojacket. The aerojacket finally gave way.

I almost got an accidental KoM today on a very hilly (8000 feet of steep climbing) 200km brevet. A 10 mile stretch in 23 minutes, just missed by a few seconds although my power level was not very high because two big climbs were coming up. I also did not wear the Giro Vanquish today, going for the one with the big honking mirror on it because some of the roads were high volume and high speed. Three flats. Lousy roads. Horrible. Nothing but huge pothole after pothole thru the National Park. 20+ miles of it. The only road that I can recall to have been worse was a road in the Dominican Republic on the way to the plant.

I got a new computer and subsequently downloaded a more recent version of GoldenCheetah that seems allow me to measure CdA differences more accurately. I re-analyzed shield vs no shield with glasses. The glasses showed a little less better. If I get the chance, I want to repeat and include the medium helmet. I don't understand my results. Why would glasses be faster.

 

[Osiris]

No, I used a PowerTap G3 hub as a power meter laced to a conventional rim covered by an aerojacket. The aerojacket finally gave way.

I almost got an accidental KoM today on a very hilly (8000 feet of steep climbing) 200km brevet. A 10 mile stretch in 23 minutes, just missed by a few seconds although my power level was not very high because two big climbs were coming up. I also did not wear the Giro Vanquish today, going for the one with the big honking mirror on it because some of the roads were high volume and high speed. Three flats. Lousy roads. Horrible. Nothing but huge pothole after pothole thru the National Park. 20+ miles of it. The only road that I can recall to have been worse was a road in the Dominican Republic on the way to the plant.

Sounds like some of the "roads" I've been on in Pennsylvania. Rumor has it that entire cars have disappeared in those, never to be seen again.

I got a new computer and subsequently downloaded a more recent version of GoldenCheetah that seems allow me to measure CdA differences more accurately. I re-analyzed shield vs no shield with glasses. The glasses showed a little less better. If I get the chance, I want to repeat and include the medium helmet. I don't understand my results. Why would glasses be faster.

If the differences are small, more testing might be called for. I recall reading some talk on a TT forum about helmets actually being slower with visors than without, but that never made sense to me. Then again, one of my high school buddies who is a rocket scientist in real life mentioned that there's a lot about aerodynamics that seems sharply counter-intuitive. Rather than trying to understand it, they just go with the data.

I spent much of the day testing my new Garmin Virb Ultra 30 video camera. It's got some really nice features, including the ability to pair itself to any wireless sensors on your bike. It also has voice activation, which is great if you have the camera mounted down by your feet, as it most commonly is on bents. All the GPS functions I rely on are now built into the camera, so in theory I could leave the GPS unit home and review all the ride data in video form. In practice, however, only the power and cadence readings work properly. The grade sensor is a joke. Not only can you climb halfway up the hill before it even senses a change in slope, but in many cases it's readings are hugely inaccurate. Sometimes I'd be going up a mild slope, and it would read 12%! At other times, it would be reading the slope in reverse, telling me I'm descending when I'm really climbing, and vice versa. Just ridiculous. Fortunately the unit I bought is a refurbished one, which I got at a huge discount. If it turns out to be just another overpriced toy, I can at least take some consolation in the fact that I got it for far below list.

 

[ed72]

If the differences are small, more testing might be called for. I recall reading some talk on a TT forum about helmets actually being slower with visors than without, but that never made sense to me.

True. I did run twice the faceshield config and each time there were six peaks on the Chung plot meaning, I went back and forth three times (over 3 miles of data). Your comment gets to Method Validation. If I were to do so, I would probably find two objects of known size and shape to attach to the bike by a thin metal rod. Run the protocol with and without the added known sized object. BTW....I was getting 0.003 difference from shielded helmet to glasses/eyewear, which I suspect is just within my limit to detect a difference in configuration. To put it into perspective, my total quest for aero improvement was 0.010 or about three times the presumed helmet gain. This would have gotten me 24 mph on around 145-150 watts on a warm, humid day.

I had forgotten how bad those roads are. On my upright with 35 mm or 32 mm Compass extra legere tires, I never had any problems. Today, I feel like my head has been nuked and I want to puke my brains out. I have to think about a different machine for randonneuring on such miserable road surfaces.